diff --git a/changelog b/changelog
index f766cd4..315c425 100644
--- a/changelog
+++ b/changelog
@@ -1,99 +1,120 @@
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20130727 tpd src/axiom-website/patches.html 20130727.01.tpd.patch
20130727 tpd src/axiom-website/CATS/index.html add rich3c
20130727 tpd src/axiom-website/CATS/rich3c.input added
diff --git a/src/axiom-website/CATS/index.html b/src/axiom-website/CATS/index.html
index cc3cf50..379e70d 100644
--- a/src/axiom-website/CATS/index.html
+++ b/src/axiom-website/CATS/index.html
@@ -389,6 +389,24 @@ They have been rewritten using Axiom syntax.
x^m (a+b x^n)^p (part 10)
source
pdf
+ (a+b x^n)^m (c+d x^n)^p
+ source
+ pdf
+ x^m (a+b x^n)^p (c+d x^n)^q (part 1)
+ source
+ pdf
+ x^m (a+b x^n)^p (c+d x^n)^q (part 2)
+ source
+ pdf
+ x^m (a+b x^n)^p (c+d x^n)^q (part 3)
+ source
+ pdf
+ x^m (a+b x^n)^p (c+d x^n)^q (part 4)
+ source
+ pdf
+ x^m (a+b x^n)^p (c+d x^n)^q (part 5)
+ source
+ pdf
Rich
diff --git a/src/axiom-website/CATS/rich5.input.pamphlet b/src/axiom-website/CATS/rich5.input.pamphlet
new file mode 100644
index 0000000..55e1b1d
--- /dev/null
+++ b/src/axiom-website/CATS/rich5.input.pamphlet
@@ -0,0 +1,22971 @@
+\documentclass{article}
+\usepackage{axiom}
+\setlength{\textwidth}{400pt}
+\begin{document}
+\title{\$SPAD/src/input rich5.input}
+\author{Albert Rich and Timothy Daly}
+\maketitle
+\begin{abstract}
+\verb|(a+b*x^n)^m*(c+d*x^n)^p|
+There are:
+\begin{itemize}
+\item 173 integrals in this file.
+\item 172 supplied "optimal results".
+\item 172 matching answers.
+\item 2 cases where Axiom answer differs from Rubi
+\item 63 cases where Axiom supplied 2 results.
+\item 5 cases that Axiom failed to integrate.
+\item 56 that contain expressions Axiom does not recognize.
+\end{itemize}
+\end{abstract}
+\eject
+\tableofcontents
+\eject
+\begin{chunk}{*}
+)set break resume
+)sys rm -f rich5.output
+)spool rich5.output
+)set message test on
+)set message auto off
+)clear all
+
+--S 1 of 994
+t0:=(a+b*x^2)*(c+d*x^2)^4
+--R
+--R
+--R (1)
+--R 4 10 4 3 8 3 2 2 6 2 2 3 4
+--R b d x + (a d + 4b c d )x + (4a c d + 6b c d )x + (6a c d + 4b c d)x
+--R +
+--R 3 4 2 4
+--R (4a c d + b c )x + a c
+--R Type: Polynomial(Integer)
+--E 1
+
+--S 2 of 994
+r0:=a*c^4*x+1/3*c^3*(b*c+4*a*d)*x^3+2/5*c^2*d*(2*b*c+3*a*d)*x^5+_
+ 2/7*c*d^2*(3*b*c+2*a*d)*x^7+1/9*d^3*(4*b*c+a*d)*x^9+1/11*b*d^4*x^11
+--R
+--R
+--R (2)
+--R 1 4 11 1 4 4 3 9 4 3 6 2 2 7
+--R -- b d x + (- a d + - b c d )x + (- a c d + - b c d )x
+--R 11 9 9 7 7
+--R +
+--R 6 2 2 4 3 5 4 3 1 4 3 4
+--R (- a c d + - b c d)x + (- a c d + - b c )x + a c x
+--R 5 5 3 3
+--R Type: Polynomial(Fraction(Integer))
+--E 2
+
+--S 3 of 994
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 1 4 11 1 4 4 3 9 4 3 6 2 2 7
+--R -- b d x + (- a d + - b c d )x + (- a c d + - b c d )x
+--R 11 9 9 7 7
+--R +
+--R 6 2 2 4 3 5 4 3 1 4 3 4
+--R (- a c d + - b c d)x + (- a c d + - b c )x + a c x
+--R 5 5 3 3
+--R Type: Polynomial(Fraction(Integer))
+--E 3
+
+--S 4 of 994
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Polynomial(Fraction(Integer))
+--E 4
+
+--S 5 of 994
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Polynomial(Fraction(Integer))
+--E 5
+
+)clear all
+
+--S 6 of 994
+t0:=(a+b*x^2)*(c+d*x^2)^3
+--R
+--R
+--R (1)
+--R 3 8 3 2 6 2 2 4 2 3 2 3
+--R b d x + (a d + 3b c d )x + (3a c d + 3b c d)x + (3a c d + b c )x + a c
+--R Type: Polynomial(Integer)
+--E 6
+
+--S 7 of 994
+r0:=a*c^3*x+1/3*c^2*(b*c+3*a*d)*x^3+3/5*c*d*(b*c+a*d)*x^5+_
+ 1/7*d^2*(3*b*c+a*d)*x^7+1/9*b*d^3*x^9
+--R
+--R
+--R (2)
+--R 1 3 9 1 3 3 2 7 3 2 3 2 5
+--R - b d x + (- a d + - b c d )x + (- a c d + - b c d)x
+--R 9 7 7 5 5
+--R +
+--R 2 1 3 3 3
+--R (a c d + - b c )x + a c x
+--R 3
+--R Type: Polynomial(Fraction(Integer))
+--E 7
+
+--S 8 of 994
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 1 3 9 1 3 3 2 7 3 2 3 2 5
+--R - b d x + (- a d + - b c d )x + (- a c d + - b c d)x
+--R 9 7 7 5 5
+--R +
+--R 2 1 3 3 3
+--R (a c d + - b c )x + a c x
+--R 3
+--R Type: Polynomial(Fraction(Integer))
+--E 8
+
+--S 9 of 994
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Polynomial(Fraction(Integer))
+--E 9
+
+--S 10 of 994
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Polynomial(Fraction(Integer))
+--E 10
+
+)clear all
+
+--S 11 of 994
+t0:=(a+b*x^2)*(c+d*x^2)^2
+--R
+--R
+--R 2 6 2 4 2 2 2
+--R (1) b d x + (a d + 2b c d)x + (2a c d + b c )x + a c
+--R Type: Polynomial(Integer)
+--E 11
+
+--S 12 of 994
+r0:=a*c^2*x+1/3*c*(b*c+2*a*d)*x^3+1/5*d*(2*b*c+a*d)*x^5+1/7*b*d^2*x^7
+--R
+--R
+--R 1 2 7 1 2 2 5 2 1 2 3 2
+--R (2) - b d x + (- a d + - b c d)x + (- a c d + - b c )x + a c x
+--R 7 5 5 3 3
+--R Type: Polynomial(Fraction(Integer))
+--E 12
+
+--S 13 of 994
+a0:=integrate(t0,x)
+--R
+--R
+--R 1 2 7 1 2 2 5 2 1 2 3 2
+--R (3) - b d x + (- a d + - b c d)x + (- a c d + - b c )x + a c x
+--R 7 5 5 3 3
+--R Type: Polynomial(Fraction(Integer))
+--E 13
+
+--S 14 of 994
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Polynomial(Fraction(Integer))
+--E 14
+
+--S 15 of 994
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Polynomial(Fraction(Integer))
+--E 15
+
+)clear all
+
+--S 16 of 994
+t0:=(a+b*x^2)*(c+d*x^2)
+--R
+--R
+--R 4 2
+--R (1) b d x + (a d + b c)x + a c
+--R Type: Polynomial(Integer)
+--E 16
+
+--S 17 of 994
+r0:=a*c*x+1/3*(b*c+a*d)*x^3+1/5*b*d*x^5
+--R
+--R
+--R 1 5 1 1 3
+--R (2) - b d x + (- a d + - b c)x + a c x
+--R 5 3 3
+--R Type: Polynomial(Fraction(Integer))
+--E 17
+
+--S 18 of 994
+a0:=integrate(t0,x)
+--R
+--R
+--R 1 5 1 1 3
+--R (3) - b d x + (- a d + - b c)x + a c x
+--R 5 3 3
+--R Type: Polynomial(Fraction(Integer))
+--E 18
+
+--S 19 of 994
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Polynomial(Fraction(Integer))
+--E 19
+
+--S 20 of 994
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Polynomial(Fraction(Integer))
+--E 20
+
+)clear all
+
+--S 21 of 994
+t0:=(a+b*x^2)/(c+d*x^2)
+--R
+--R
+--R 2
+--R b x + a
+--R (1) --------
+--R 2
+--R d x + c
+--R Type: Fraction(Polynomial(Integer))
+--E 21
+
+--S 22 of 994
+r0:=b*x/d-(b*c-a*d)*atan(x*sqrt(d)/sqrt(c))/(d^(3/2)*sqrt(c))
+--R
+--R
+--R +-+
+--R x\|d +-+ +-+
+--R (a d - b c)atan(-----) + b x\|c \|d
+--R +-+
+--R \|c
+--R (2) ------------------------------------
+--R +-+ +-+
+--R d\|c \|d
+--R Type: Expression(Integer)
+--E 22
+
+--S 23 of 994
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 2 +-----+
+--R (d x - c)\|- c d + 2c d x +-----+
+--R (a d - b c)log(---------------------------) + 2b x\|- c d
+--R 2
+--R d x + c
+--R [----------------------------------------------------------,
+--R +-----+
+--R 2d\|- c d
+--R +---+
+--R x\|c d +---+
+--R (a d - b c)atan(-------) + b x\|c d
+--R c
+--R ------------------------------------]
+--R +---+
+--R d\|c d
+--R Type: Union(List(Expression(Integer)),...)
+--E 23
+
+--S 24 of 994
+m0a:=a0.1-r0
+--R
+--R
+--R (4)
+--R 2 +-----+
+--R +-+ +-+ (d x - c)\|- c d + 2c d x
+--R (a d - b c)\|c \|d log(---------------------------)
+--R 2
+--R d x + c
+--R +
+--R +-+
+--R +-----+ x\|d
+--R (- 2a d + 2b c)\|- c d atan(-----)
+--R +-+
+--R \|c
+--R /
+--R +-----+ +-+ +-+
+--R 2d\|- c d \|c \|d
+--R Type: Expression(Integer)
+--E 24
+
+--S 25 of 994
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 25
+
+--S 26 of 994
+m0b:=a0.2-r0
+--R
+--R
+--R +---+ +-+
+--R +-+ +-+ x\|c d +---+ x\|d
+--R (a d - b c)\|c \|d atan(-------) + (- a d + b c)\|c d atan(-----)
+--R c +-+
+--R \|c
+--R (6) -----------------------------------------------------------------
+--R +-+ +-+ +---+
+--R d\|c \|d \|c d
+--R Type: Expression(Integer)
+--E 26
+
+--S 27 of 994
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 27
+
+)clear all
+
+--S 28 of 994
+t0:=(a+b*x^2)/(c+d*x^2)^2
+--R
+--R
+--R 2
+--R b x + a
+--R (1) -------------------
+--R 2 4 2 2
+--R d x + 2c d x + c
+--R Type: Fraction(Polynomial(Integer))
+--E 28
+
+--S 29 of 994
+r0:=-1/2*(b*c-a*d)*x/(c*d*(c+d*x^2))+1/2*(b*c+a*d)*_
+ atan(x*sqrt(d)/sqrt(c))/(c^(3/2)*d^(3/2))
+--R
+--R
+--R +-+
+--R 2 2 2 x\|d +-+ +-+
+--R ((a d + b c d)x + a c d + b c )atan(-----) + (a d - b c)x\|c \|d
+--R +-+
+--R \|c
+--R (2) -------------------------------------------------------------------
+--R 2 2 2 +-+ +-+
+--R (2c d x + 2c d)\|c \|d
+--R Type: Expression(Integer)
+--E 29
+
+--S 30 of 994
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R 2 +-----+
+--R 2 2 2 (d x - c)\|- c d + 2c d x
+--R ((a d + b c d)x + a c d + b c )log(---------------------------)
+--R 2
+--R d x + c
+--R +
+--R +-----+
+--R (2a d - 2b c)x\|- c d
+--R /
+--R 2 2 2 +-----+
+--R (4c d x + 4c d)\|- c d
+--R ,
+--R +---+
+--R 2 2 2 x\|c d +---+
+--R ((a d + b c d)x + a c d + b c )atan(-------) + (a d - b c)x\|c d
+--R c
+--R -------------------------------------------------------------------]
+--R 2 2 2 +---+
+--R (2c d x + 2c d)\|c d
+--R Type: Union(List(Expression(Integer)),...)
+--E 30
+
+--S 31 of 994
+m0a:=a0.1-r0
+--R
+--R
+--R (4)
+--R 2 +-----+
+--R +-+ +-+ (d x - c)\|- c d + 2c d x
+--R (a d + b c)\|c \|d log(---------------------------)
+--R 2
+--R d x + c
+--R +
+--R +-+
+--R +-----+ x\|d
+--R (- 2a d - 2b c)\|- c d atan(-----)
+--R +-+
+--R \|c
+--R /
+--R +-----+ +-+ +-+
+--R 4c d\|- c d \|c \|d
+--R Type: Expression(Integer)
+--E 31
+
+--S 32 of 994
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 32
+
+--S 33 of 994
+m0b:=a0.2-r0
+--R
+--R
+--R +---+ +-+
+--R +-+ +-+ x\|c d +---+ x\|d
+--R (a d + b c)\|c \|d atan(-------) + (- a d - b c)\|c d atan(-----)
+--R c +-+
+--R \|c
+--R (6) -----------------------------------------------------------------
+--R +-+ +-+ +---+
+--R 2c d\|c \|d \|c d
+--R Type: Expression(Integer)
+--E 33
+
+--S 34 of 994
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 34
+
+)clear all
+
+--S 35 of 994
+t0:=(a+b*x^2)/(c+d*x^2)^3
+--R
+--R
+--R 2
+--R b x + a
+--R (1) -----------------------------
+--R 3 6 2 4 2 2 3
+--R d x + 3c d x + 3c d x + c
+--R Type: Fraction(Polynomial(Integer))
+--E 35
+
+--S 36 of 994
+r0:=-1/4*(b*c-a*d)*x/(c*d*(c+d*x^2)^2)+1/8*(b*c+3*a*d)*x/(c^2*_
+ d*(c+d*x^2))+1/8*(b*c+3*a*d)*atan(x*sqrt(d)/sqrt(c))/(c^(5/2)*d^(3/2))
+--R
+--R
+--R (2)
+--R +-+
+--R 3 2 4 2 2 2 2 3 x\|d
+--R ((3a d + b c d )x + (6a c d + 2b c d)x + 3a c d + b c )atan(-----)
+--R +-+
+--R \|c
+--R +
+--R 2 3 2 +-+ +-+
+--R ((3a d + b c d)x + (5a c d - b c )x)\|c \|d
+--R /
+--R 2 3 4 3 2 2 4 +-+ +-+
+--R (8c d x + 16c d x + 8c d)\|c \|d
+--R Type: Expression(Integer)
+--E 36
+
+--S 37 of 994
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R 3 2 4 2 2 2 2 3
+--R ((3a d + b c d )x + (6a c d + 2b c d)x + 3a c d + b c )
+--R *
+--R 2 +-----+
+--R (d x - c)\|- c d + 2c d x
+--R log(---------------------------)
+--R 2
+--R d x + c
+--R +
+--R 2 3 2 +-----+
+--R ((6a d + 2b c d)x + (10a c d - 2b c )x)\|- c d
+--R /
+--R 2 3 4 3 2 2 4 +-----+
+--R (16c d x + 32c d x + 16c d)\|- c d
+--R ,
+--R
+--R 3 2 4 2 2 2 2 3
+--R ((3a d + b c d )x + (6a c d + 2b c d)x + 3a c d + b c )
+--R *
+--R +---+
+--R x\|c d
+--R atan(-------)
+--R c
+--R +
+--R 2 3 2 +---+
+--R ((3a d + b c d)x + (5a c d - b c )x)\|c d
+--R /
+--R 2 3 4 3 2 2 4 +---+
+--R (8c d x + 16c d x + 8c d)\|c d
+--R ]
+--R Type: Union(List(Expression(Integer)),...)
+--E 37
+
+--S 38 of 994
+m0a:=a0.1-r0
+--R
+--R
+--R (4)
+--R 2 +-----+
+--R +-+ +-+ (d x - c)\|- c d + 2c d x
+--R (3a d + b c)\|c \|d log(---------------------------)
+--R 2
+--R d x + c
+--R +
+--R +-+
+--R +-----+ x\|d
+--R (- 6a d - 2b c)\|- c d atan(-----)
+--R +-+
+--R \|c
+--R /
+--R 2 +-----+ +-+ +-+
+--R 16c d\|- c d \|c \|d
+--R Type: Expression(Integer)
+--E 38
+
+--S 39 of 994
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 39
+
+--S 40 of 994
+m0b:=a0.2-r0
+--R
+--R
+--R +---+ +-+
+--R +-+ +-+ x\|c d +---+ x\|d
+--R (3a d + b c)\|c \|d atan(-------) + (- 3a d - b c)\|c d atan(-----)
+--R c +-+
+--R \|c
+--R (6) -------------------------------------------------------------------
+--R 2 +-+ +-+ +---+
+--R 8c d\|c \|d \|c d
+--R Type: Expression(Integer)
+--E 40
+
+--S 41 of 994
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 41
+
+)clear all
+
+--S 42 of 994
+t0:=(a+b*x^2)^2*(c+d*x^2)^3
+--R
+--R
+--R (1)
+--R 2 3 10 3 2 2 8 2 3 2 2 2 6
+--R b d x + (2a b d + 3b c d )x + (a d + 6a b c d + 3b c d)x
+--R +
+--R 2 2 2 2 3 4 2 2 3 2 2 3
+--R (3a c d + 6a b c d + b c )x + (3a c d + 2a b c )x + a c
+--R Type: Polynomial(Integer)
+--E 42
+
+--S 43 of 994
+r0:=a^2*c^3*x+1/3*a*c^2*(2*b*c+3*a*d)*x^3+1/5*c*(b^2*c^2+6*a*b*c*d+_
+ 3*a^2*d^2)*x^5+1/7*d*(3*b^2*c^2+6*a*b*c*d+a^2*d^2)*x^7+_
+ 1/9*b*d^2*(3*b*c+2*a*d)*x^9+1/11*b^2*d^3*x^11
+--R
+--R
+--R (2)
+--R 1 2 3 11 2 3 1 2 2 9 1 2 3 6 2 3 2 2 7
+--R -- b d x + (- a b d + - b c d )x + (- a d + - a b c d + - b c d)x
+--R 11 9 3 7 7 7
+--R +
+--R 3 2 2 6 2 1 2 3 5 2 2 2 3 3 2 3
+--R (- a c d + - a b c d + - b c )x + (a c d + - a b c )x + a c x
+--R 5 5 5 3
+--R Type: Polynomial(Fraction(Integer))
+--E 43
+
+--S 44 of 994
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 1 2 3 11 2 3 1 2 2 9 1 2 3 6 2 3 2 2 7
+--R -- b d x + (- a b d + - b c d )x + (- a d + - a b c d + - b c d)x
+--R 11 9 3 7 7 7
+--R +
+--R 3 2 2 6 2 1 2 3 5 2 2 2 3 3 2 3
+--R (- a c d + - a b c d + - b c )x + (a c d + - a b c )x + a c x
+--R 5 5 5 3
+--R Type: Polynomial(Fraction(Integer))
+--E 44
+
+--S 45 of 994
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Polynomial(Fraction(Integer))
+--E 45
+
+--S 46 of 994
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Polynomial(Fraction(Integer))
+--E 46
+
+)clear all
+
+--S 47 of 994
+t0:=(a+b*x^2)^2*(c+d*x^2)^2
+--R
+--R
+--R (1)
+--R 2 2 8 2 2 6 2 2 2 2 4
+--R b d x + (2a b d + 2b c d)x + (a d + 4a b c d + b c )x
+--R +
+--R 2 2 2 2 2
+--R (2a c d + 2a b c )x + a c
+--R Type: Polynomial(Integer)
+--E 47
+
+--S 48 of 994
+r0:=a^2*c^2*x+2/3*a*c*(b*c+a*d)*x^3+1/5*(b^2*c^2+4*a*b*c*d+a^2*d^2)*x^5+_
+ 2/7*b*d*(b*c+a*d)*x^7+1/9*b^2*d^2*x^9
+--R
+--R
+--R (2)
+--R 1 2 2 9 2 2 2 2 7 1 2 2 4 1 2 2 5
+--R - b d x + (- a b d + - b c d)x + (- a d + - a b c d + - b c )x
+--R 9 7 7 5 5 5
+--R +
+--R 2 2 2 2 3 2 2
+--R (- a c d + - a b c )x + a c x
+--R 3 3
+--R Type: Polynomial(Fraction(Integer))
+--E 48
+
+--S 49 of 994
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 1 2 2 9 2 2 2 2 7 1 2 2 4 1 2 2 5
+--R - b d x + (- a b d + - b c d)x + (- a d + - a b c d + - b c )x
+--R 9 7 7 5 5 5
+--R +
+--R 2 2 2 2 3 2 2
+--R (- a c d + - a b c )x + a c x
+--R 3 3
+--R Type: Polynomial(Fraction(Integer))
+--E 49
+
+--S 50 of 994
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Polynomial(Fraction(Integer))
+--E 50
+
+--S 51 of 994
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Polynomial(Fraction(Integer))
+--E 51
+
+)clear all
+
+--S 52 of 994
+t0:=(a+b*x^2)^2*(c+d*x^2)
+--R
+--R
+--R 2 6 2 4 2 2 2
+--R (1) b d x + (2a b d + b c)x + (a d + 2a b c)x + a c
+--R Type: Polynomial(Integer)
+--E 52
+
+--S 53 of 994
+r0:=a^2*c*x+1/3*a*(2*b*c+a*d)*x^3+1/5*b*(b*c+2*a*d)*x^5+1/7*b^2*d*x^7
+--R
+--R
+--R 1 2 7 2 1 2 5 1 2 2 3 2
+--R (2) - b d x + (- a b d + - b c)x + (- a d + - a b c)x + a c x
+--R 7 5 5 3 3
+--R Type: Polynomial(Fraction(Integer))
+--E 53
+
+--S 54 of 994
+a0:=integrate(t0,x)
+--R
+--R
+--R 1 2 7 2 1 2 5 1 2 2 3 2
+--R (3) - b d x + (- a b d + - b c)x + (- a d + - a b c)x + a c x
+--R 7 5 5 3 3
+--R Type: Polynomial(Fraction(Integer))
+--E 54
+
+--S 55 of 994
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Polynomial(Fraction(Integer))
+--E 55
+
+--S 56 of 994
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Polynomial(Fraction(Integer))
+--E 56
+
+)clear all
+
+--S 57 of 994
+t0:=(a+b*x^2)^2/(c+d*x^2)
+--R
+--R
+--R 2 4 2 2
+--R b x + 2a b x + a
+--R (1) -------------------
+--R 2
+--R d x + c
+--R Type: Fraction(Polynomial(Integer))
+--E 57
+
+--S 58 of 994
+r0:=-b*(b*c-2*a*d)*x/d^2+1/3*b^2*x^3/d+(b*c-a*d)^2*atan(x*sqrt(d)/_
+ sqrt(c))/(d^(5/2)*sqrt(c))
+--R
+--R
+--R (2)
+--R +-+
+--R 2 2 2 2 x\|d 2 3 2 +-+ +-+
+--R (3a d - 6a b c d + 3b c )atan(-----) + (b d x + (6a b d - 3b c)x)\|c \|d
+--R +-+
+--R \|c
+--R ---------------------------------------------------------------------------
+--R 2 +-+ +-+
+--R 3d \|c \|d
+--R Type: Expression(Integer)
+--E 58
+
+--S 59 of 994
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R 2 +-----+
+--R 2 2 2 2 (d x - c)\|- c d + 2c d x
+--R (3a d - 6a b c d + 3b c )log(---------------------------)
+--R 2
+--R d x + c
+--R +
+--R 2 3 2 +-----+
+--R (2b d x + (12a b d - 6b c)x)\|- c d
+--R /
+--R 2 +-----+
+--R 6d \|- c d
+--R ,
+--R +---+
+--R 2 2 2 2 x\|c d 2 3 2 +---+
+--R (3a d - 6a b c d + 3b c )atan(-------) + (b d x + (6a b d - 3b c)x)\|c d
+--R c
+--R ---------------------------------------------------------------------------]
+--R 2 +---+
+--R 3d \|c d
+--R Type: Union(List(Expression(Integer)),...)
+--E 59
+
+--S 60 of 994
+m0a:=a0.1-r0
+--R
+--R
+--R (4)
+--R 2 +-----+
+--R 2 2 2 2 +-+ +-+ (d x - c)\|- c d + 2c d x
+--R (a d - 2a b c d + b c )\|c \|d log(---------------------------)
+--R 2
+--R d x + c
+--R +
+--R +-+
+--R 2 2 2 2 +-----+ x\|d
+--R (- 2a d + 4a b c d - 2b c )\|- c d atan(-----)
+--R +-+
+--R \|c
+--R /
+--R 2 +-----+ +-+ +-+
+--R 2d \|- c d \|c \|d
+--R Type: Expression(Integer)
+--E 60
+
+--S 61 of 994
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 61
+
+--S 62 of 994
+m0b:=a0.2-r0
+--R
+--R
+--R (6)
+--R +---+
+--R 2 2 2 2 +-+ +-+ x\|c d
+--R (a d - 2a b c d + b c )\|c \|d atan(-------)
+--R c
+--R +
+--R +-+
+--R 2 2 2 2 +---+ x\|d
+--R (- a d + 2a b c d - b c )\|c d atan(-----)
+--R +-+
+--R \|c
+--R /
+--R 2 +-+ +-+ +---+
+--R d \|c \|d \|c d
+--R Type: Expression(Integer)
+--E 62
+
+--S 63 of 994
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 63
+
+)clear all
+
+--S 64 of 994
+t0:=(a+b*x^2)^2/(c+d*x^2)^2
+--R
+--R
+--R 2 4 2 2
+--R b x + 2a b x + a
+--R (1) -------------------
+--R 2 4 2 2
+--R d x + 2c d x + c
+--R Type: Fraction(Polynomial(Integer))
+--E 64
+
+--S 65 of 994
+r0:=b^2*x/d^2+1/2*(b*c-a*d)^2*x/(c*d^2*(c+d*x^2))-1/2*(b*c-a*d)*_
+ (3*b*c+a*d)*atan(x*sqrt(d)/sqrt(c))/(c^(3/2)*d^(5/2))
+--R
+--R
+--R (2)
+--R +-+
+--R 2 3 2 2 2 2 2 2 2 2 3 x\|d
+--R ((a d + 2a b c d - 3b c d)x + a c d + 2a b c d - 3b c )atan(-----)
+--R +-+
+--R \|c
+--R +
+--R 2 3 2 2 2 2 +-+ +-+
+--R (2b c d x + (a d - 2a b c d + 3b c )x)\|c \|d
+--R /
+--R 3 2 2 2 +-+ +-+
+--R (2c d x + 2c d )\|c \|d
+--R Type: Expression(Integer)
+--E 65
+
+--S 66 of 994
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R 2 3 2 2 2 2 2 2 2 2 3
+--R ((a d + 2a b c d - 3b c d)x + a c d + 2a b c d - 3b c )
+--R *
+--R 2 +-----+
+--R (d x - c)\|- c d + 2c d x
+--R log(---------------------------)
+--R 2
+--R d x + c
+--R +
+--R 2 3 2 2 2 2 +-----+
+--R (4b c d x + (2a d - 4a b c d + 6b c )x)\|- c d
+--R /
+--R 3 2 2 2 +-----+
+--R (4c d x + 4c d )\|- c d
+--R ,
+--R
+--R 2 3 2 2 2 2 2 2 2 2 3
+--R ((a d + 2a b c d - 3b c d)x + a c d + 2a b c d - 3b c )
+--R *
+--R +---+
+--R x\|c d
+--R atan(-------)
+--R c
+--R +
+--R 2 3 2 2 2 2 +---+
+--R (2b c d x + (a d - 2a b c d + 3b c )x)\|c d
+--R /
+--R 3 2 2 2 +---+
+--R (2c d x + 2c d )\|c d
+--R ]
+--R Type: Union(List(Expression(Integer)),...)
+--E 66
+
+--S 67 of 994
+m0a:=a0.1-r0
+--R
+--R
+--R (4)
+--R 2 +-----+
+--R 2 2 2 2 +-+ +-+ (d x - c)\|- c d + 2c d x
+--R (a d + 2a b c d - 3b c )\|c \|d log(---------------------------)
+--R 2
+--R d x + c
+--R +
+--R +-+
+--R 2 2 2 2 +-----+ x\|d
+--R (- 2a d - 4a b c d + 6b c )\|- c d atan(-----)
+--R +-+
+--R \|c
+--R /
+--R 2 +-----+ +-+ +-+
+--R 4c d \|- c d \|c \|d
+--R Type: Expression(Integer)
+--E 67
+
+--S 68 of 994
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 68
+
+--S 69 of 994
+m0b:=a0.2-r0
+--R
+--R
+--R (6)
+--R +---+
+--R 2 2 2 2 +-+ +-+ x\|c d
+--R (a d + 2a b c d - 3b c )\|c \|d atan(-------)
+--R c
+--R +
+--R +-+
+--R 2 2 2 2 +---+ x\|d
+--R (- a d - 2a b c d + 3b c )\|c d atan(-----)
+--R +-+
+--R \|c
+--R /
+--R 2 +-+ +-+ +---+
+--R 2c d \|c \|d \|c d
+--R Type: Expression(Integer)
+--E 69
+
+--S 70 of 994
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 70
+
+)clear all
+
+--S 71 of 994
+t0:=(a+b*x^2)^2/(c+d*x^2)^3
+--R
+--R
+--R 2 4 2 2
+--R b x + 2a b x + a
+--R (1) -----------------------------
+--R 3 6 2 4 2 2 3
+--R d x + 3c d x + 3c d x + c
+--R Type: Fraction(Polynomial(Integer))
+--E 71
+
+--S 72 of 994
+r0:=-1/4*(b*c-a*d)*x*(a+b*x^2)/(c*d*(c+d*x^2)^2)+3/8*(a^2/c^2-b^2/d^2)*x/_
+ (c+d*x^2)+1/8*(3*b^2*c^2+2*a*b*c*d+3*a^2*d^2)*atan(x*sqrt(d)/_
+ sqrt(c))/(c^(5/2)*d^(5/2))
+--R
+--R
+--R (2)
+--R 2 4 3 2 2 2 4 2 3 2 2 2 3 2
+--R (3a d + 2a b c d + 3b c d )x + (6a c d + 4a b c d + 6b c d)x
+--R +
+--R 2 2 2 3 2 4
+--R 3a c d + 2a b c d + 3b c
+--R *
+--R +-+
+--R x\|d
+--R atan(-----)
+--R +-+
+--R \|c
+--R +
+--R 2 3 2 2 2 3 2 2 2 2 3 +-+ +-+
+--R ((3a d + 2a b c d - 5b c d)x + (5a c d - 2a b c d - 3b c )x)\|c \|d
+--R /
+--R 2 4 4 3 3 2 4 2 +-+ +-+
+--R (8c d x + 16c d x + 8c d )\|c \|d
+--R Type: Expression(Integer)
+--E 72
+
+--S 73 of 994
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R 2 4 3 2 2 2 4 2 3 2 2 2 3 2
+--R (3a d + 2a b c d + 3b c d )x + (6a c d + 4a b c d + 6b c d)x
+--R +
+--R 2 2 2 3 2 4
+--R 3a c d + 2a b c d + 3b c
+--R *
+--R 2 +-----+
+--R (d x - c)\|- c d + 2c d x
+--R log(---------------------------)
+--R 2
+--R d x + c
+--R +
+--R 2 3 2 2 2 3 2 2 2 2 3
+--R ((6a d + 4a b c d - 10b c d)x + (10a c d - 4a b c d - 6b c )x)
+--R *
+--R +-----+
+--R \|- c d
+--R /
+--R 2 4 4 3 3 2 4 2 +-----+
+--R (16c d x + 32c d x + 16c d )\|- c d
+--R ,
+--R
+--R 2 4 3 2 2 2 4 2 3 2 2 2 3 2
+--R (3a d + 2a b c d + 3b c d )x + (6a c d + 4a b c d + 6b c d)x
+--R +
+--R 2 2 2 3 2 4
+--R 3a c d + 2a b c d + 3b c
+--R *
+--R +---+
+--R x\|c d
+--R atan(-------)
+--R c
+--R +
+--R 2 3 2 2 2 3 2 2 2 2 3 +---+
+--R ((3a d + 2a b c d - 5b c d)x + (5a c d - 2a b c d - 3b c )x)\|c d
+--R /
+--R 2 4 4 3 3 2 4 2 +---+
+--R (8c d x + 16c d x + 8c d )\|c d
+--R ]
+--R Type: Union(List(Expression(Integer)),...)
+--E 73
+
+--S 74 of 994
+m0a:=a0.1-r0
+--R
+--R
+--R (4)
+--R 2 +-----+
+--R 2 2 2 2 +-+ +-+ (d x - c)\|- c d + 2c d x
+--R (3a d + 2a b c d + 3b c )\|c \|d log(---------------------------)
+--R 2
+--R d x + c
+--R +
+--R +-+
+--R 2 2 2 2 +-----+ x\|d
+--R (- 6a d - 4a b c d - 6b c )\|- c d atan(-----)
+--R +-+
+--R \|c
+--R /
+--R 2 2 +-----+ +-+ +-+
+--R 16c d \|- c d \|c \|d
+--R Type: Expression(Integer)
+--E 74
+
+--S 75 of 994
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 75
+
+--S 76 of 994
+m0b:=a0.2-r0
+--R
+--R
+--R (6)
+--R +---+
+--R 2 2 2 2 +-+ +-+ x\|c d
+--R (3a d + 2a b c d + 3b c )\|c \|d atan(-------)
+--R c
+--R +
+--R +-+
+--R 2 2 2 2 +---+ x\|d
+--R (- 3a d - 2a b c d - 3b c )\|c d atan(-----)
+--R +-+
+--R \|c
+--R /
+--R 2 2 +-+ +-+ +---+
+--R 8c d \|c \|d \|c d
+--R Type: Expression(Integer)
+--E 76
+
+--S 77 of 994
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 77
+
+)clear all
+
+--S 78 of 994
+t0:=(a+b*x^2)^3*(c+d*x^2)^3
+--R
+--R
+--R (1)
+--R 3 3 12 2 3 3 2 10 2 3 2 2 3 2 8
+--R b d x + (3a b d + 3b c d )x + (3a b d + 9a b c d + 3b c d)x
+--R +
+--R 3 3 2 2 2 2 3 3 6 3 2 2 2 2 3 4
+--R (a d + 9a b c d + 9a b c d + b c )x + (3a c d + 9a b c d + 3a b c )x
+--R +
+--R 3 2 2 3 2 3 3
+--R (3a c d + 3a b c )x + a c
+--R Type: Polynomial(Integer)
+--E 78
+
+--S 79 of 994
+r0:=a^3*c^3*x+a^2*c^2*(b*c+a*d)*x^3+3/5*a*c*(b^2*c^2+3*a*b*c*d+a^2*d^2)*_
+ x^5+1/7*(b*c+a*d)*(b^2*c^2+8*a*b*c*d+a^2*d^2)*x^7+1/3*b*d*_
+ (b^2*c^2+3*a*b*c*d+a^2*d^2)*x^9+3/11*b^2*d^2*(b*c+a*d)*x^11+_
+ 1/13*b^3*d^3*x^13
+--R
+--R
+--R (2)
+--R 1 3 3 13 3 2 3 3 3 2 11 1 2 3 2 2 1 3 2 9
+--R -- b d x + (-- a b d + -- b c d )x + (- a b d + a b c d + - b c d)x
+--R 13 11 11 3 3
+--R +
+--R 1 3 3 9 2 2 9 2 2 1 3 3 7
+--R (- a d + - a b c d + - a b c d + - b c )x
+--R 7 7 7 7
+--R +
+--R 3 3 2 9 2 2 3 2 3 5 3 2 2 3 3 3 3
+--R (- a c d + - a b c d + - a b c )x + (a c d + a b c )x + a c x
+--R 5 5 5
+--R Type: Polynomial(Fraction(Integer))
+--E 79
+
+--S 80 of 994
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 1 3 3 13 3 2 3 3 3 2 11 1 2 3 2 2 1 3 2 9
+--R -- b d x + (-- a b d + -- b c d )x + (- a b d + a b c d + - b c d)x
+--R 13 11 11 3 3
+--R +
+--R 1 3 3 9 2 2 9 2 2 1 3 3 7
+--R (- a d + - a b c d + - a b c d + - b c )x
+--R 7 7 7 7
+--R +
+--R 3 3 2 9 2 2 3 2 3 5 3 2 2 3 3 3 3
+--R (- a c d + - a b c d + - a b c )x + (a c d + a b c )x + a c x
+--R 5 5 5
+--R Type: Polynomial(Fraction(Integer))
+--E 80
+
+--S 81 of 994
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Polynomial(Fraction(Integer))
+--E 81
+
+--S 82 of 994
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Polynomial(Fraction(Integer))
+--E 82
+
+)clear all
+
+--S 83 of 994
+t0:=(a+b*x^2)^3*(c+d*x^2)^2
+--R
+--R
+--R (1)
+--R 3 2 10 2 2 3 8 2 2 2 3 2 6
+--R b d x + (3a b d + 2b c d)x + (3a b d + 6a b c d + b c )x
+--R +
+--R 3 2 2 2 2 4 3 2 2 2 3 2
+--R (a d + 6a b c d + 3a b c )x + (2a c d + 3a b c )x + a c
+--R Type: Polynomial(Integer)
+--E 83
+
+--S 84 of 994
+r0:=a^3*c^2*x+1/3*a^2*c*(3*b*c+2*a*d)*x^3+1/5*a*(3*b^2*c^2+6*a*b*c*d+_
+ a^2*d^2)*x^5+1/7*b*(b^2*c^2+6*a*b*c*d+3*a^2*d^2)*x^7+_
+ 1/9*b^2*d*(2*b*c+3*a*d)*x^9+1/11*b^3*d^2*x^11
+--R
+--R
+--R (2)
+--R 1 3 2 11 1 2 2 2 3 9 3 2 2 6 2 1 3 2 7
+--R -- b d x + (- a b d + - b c d)x + (- a b d + - a b c d + - b c )x
+--R 11 3 9 7 7 7
+--R +
+--R 1 3 2 6 2 3 2 2 5 2 3 2 2 3 3 2
+--R (- a d + - a b c d + - a b c )x + (- a c d + a b c )x + a c x
+--R 5 5 5 3
+--R Type: Polynomial(Fraction(Integer))
+--E 84
+
+--S 85 of 994
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 1 3 2 11 1 2 2 2 3 9 3 2 2 6 2 1 3 2 7
+--R -- b d x + (- a b d + - b c d)x + (- a b d + - a b c d + - b c )x
+--R 11 3 9 7 7 7
+--R +
+--R 1 3 2 6 2 3 2 2 5 2 3 2 2 3 3 2
+--R (- a d + - a b c d + - a b c )x + (- a c d + a b c )x + a c x
+--R 5 5 5 3
+--R Type: Polynomial(Fraction(Integer))
+--E 85
+
+--S 86 of 994
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Polynomial(Fraction(Integer))
+--E 86
+
+--S 87 of 994
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Polynomial(Fraction(Integer))
+--E 87
+
+)clear all
+
+--S 88 of 994
+t0:=(a+b*x^2)^3*(c+d*x^2)
+--R
+--R
+--R (1)
+--R 3 8 2 3 6 2 2 4 3 2 2 3
+--R b d x + (3a b d + b c)x + (3a b d + 3a b c)x + (a d + 3a b c)x + a c
+--R Type: Polynomial(Integer)
+--E 88
+
+--S 89 of 994
+r0:=a^3*c*x+1/3*a^2*(3*b*c+a*d)*x^3+3/5*a*b*(b*c+a*d)*x^5+_
+ 1/7*b^2*(b*c+3*a*d)*x^7+1/9*b^3*d*x^9
+--R
+--R
+--R (2)
+--R 1 3 9 3 2 1 3 7 3 2 3 2 5 1 3 2 3
+--R - b d x + (- a b d + - b c)x + (- a b d + - a b c)x + (- a d + a b c)x
+--R 9 7 7 5 5 3
+--R +
+--R 3
+--R a c x
+--R Type: Polynomial(Fraction(Integer))
+--E 89
+
+--S 90 of 994
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 1 3 9 3 2 1 3 7 3 2 3 2 5 1 3 2 3
+--R - b d x + (- a b d + - b c)x + (- a b d + - a b c)x + (- a d + a b c)x
+--R 9 7 7 5 5 3
+--R +
+--R 3
+--R a c x
+--R Type: Polynomial(Fraction(Integer))
+--E 90
+
+--S 91 of 994
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Polynomial(Fraction(Integer))
+--E 91
+
+--S 92 of 994
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Polynomial(Fraction(Integer))
+--E 92
+
+)clear all
+
+--S 93 of 994
+t0:=(a+b*x^2)^3/(c+d*x^2)
+--R
+--R
+--R 3 6 2 4 2 2 3
+--R b x + 3a b x + 3a b x + a
+--R (1) -----------------------------
+--R 2
+--R d x + c
+--R Type: Fraction(Polynomial(Integer))
+--E 93
+
+--S 94 of 994
+r0:=b*(b^2*c^2-3*a*b*c*d+3*a^2*d^2)*x/d^3-1/3*b^2*(b*c-3*a*d)*x^3/d^2+_
+ 1/5*b^3*x^5/d-(b*c-a*d)^3*atan(x*sqrt(d)/sqrt(c))/(d^(7/2)*sqrt(c))
+--R
+--R
+--R (2)
+--R +-+
+--R 3 3 2 2 2 2 3 3 x\|d
+--R (15a d - 45a b c d + 45a b c d - 15b c )atan(-----)
+--R +-+
+--R \|c
+--R +
+--R 3 2 5 2 2 3 3 2 2 2 3 2
+--R (3b d x + (15a b d - 5b c d)x + (45a b d - 45a b c d + 15b c )x)
+--R *
+--R +-+ +-+
+--R \|c \|d
+--R /
+--R 3 +-+ +-+
+--R 15d \|c \|d
+--R Type: Expression(Integer)
+--E 94
+
+--S 95 of 994
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R 3 3 2 2 2 2 3 3
+--R (15a d - 45a b c d + 45a b c d - 15b c )
+--R *
+--R 2 +-----+
+--R (d x - c)\|- c d + 2c d x
+--R log(---------------------------)
+--R 2
+--R d x + c
+--R +
+--R 3 2 5 2 2 3 3 2 2 2 3 2
+--R (6b d x + (30a b d - 10b c d)x + (90a b d - 90a b c d + 30b c )x)
+--R *
+--R +-----+
+--R \|- c d
+--R /
+--R 3 +-----+
+--R 30d \|- c d
+--R ,
+--R
+--R +---+
+--R 3 3 2 2 2 2 3 3 x\|c d
+--R (15a d - 45a b c d + 45a b c d - 15b c )atan(-------)
+--R c
+--R +
+--R 3 2 5 2 2 3 3 2 2 2 3 2
+--R (3b d x + (15a b d - 5b c d)x + (45a b d - 45a b c d + 15b c )x)
+--R *
+--R +---+
+--R \|c d
+--R /
+--R 3 +---+
+--R 15d \|c d
+--R ]
+--R Type: Union(List(Expression(Integer)),...)
+--E 95
+
+--S 96 of 994
+m0a:=a0.1-r0
+--R
+--R
+--R (4)
+--R 3 3 2 2 2 2 3 3 +-+ +-+
+--R (a d - 3a b c d + 3a b c d - b c )\|c \|d
+--R *
+--R 2 +-----+
+--R (d x - c)\|- c d + 2c d x
+--R log(---------------------------)
+--R 2
+--R d x + c
+--R +
+--R +-+
+--R 3 3 2 2 2 2 3 3 +-----+ x\|d
+--R (- 2a d + 6a b c d - 6a b c d + 2b c )\|- c d atan(-----)
+--R +-+
+--R \|c
+--R /
+--R 3 +-----+ +-+ +-+
+--R 2d \|- c d \|c \|d
+--R Type: Expression(Integer)
+--E 96
+
+--S 97 of 994
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 97
+
+--S 98 of 994
+m0b:=a0.2-r0
+--R
+--R
+--R (6)
+--R +---+
+--R 3 3 2 2 2 2 3 3 +-+ +-+ x\|c d
+--R (a d - 3a b c d + 3a b c d - b c )\|c \|d atan(-------)
+--R c
+--R +
+--R +-+
+--R 3 3 2 2 2 2 3 3 +---+ x\|d
+--R (- a d + 3a b c d - 3a b c d + b c )\|c d atan(-----)
+--R +-+
+--R \|c
+--R /
+--R 3 +-+ +-+ +---+
+--R d \|c \|d \|c d
+--R Type: Expression(Integer)
+--E 98
+
+--S 99 of 994
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 99
+
+)clear all
+
+--S 100 of 994
+t0:=(a+b*x^2)^3/(c+d*x^2)^2
+--R
+--R
+--R 3 6 2 4 2 2 3
+--R b x + 3a b x + 3a b x + a
+--R (1) -----------------------------
+--R 2 4 2 2
+--R d x + 2c d x + c
+--R Type: Fraction(Polynomial(Integer))
+--E 100
+
+--S 101 of 994
+r0:=-b^2*(2*b*c-3*a*d)*x/d^3+1/3*b^3*x^3/d^2-1/2*(b*c-a*d)^3*_
+ x/(c*d^3*(c+d*x^2))+1/2*(b*c-a*d)^2*(5*b*c+a*d)*atan(x*sqrt(d)/_
+ sqrt(c))/(c^(3/2)*d^(7/2))
+--R
+--R
+--R (2)
+--R 3 4 2 3 2 2 2 3 3 2 3 3 2 2 2
+--R (3a d + 9a b c d - 27a b c d + 15b c d)x + 3a c d + 9a b c d
+--R +
+--R 2 3 3 4
+--R - 27a b c d + 15b c
+--R *
+--R +-+
+--R x\|d
+--R atan(-----)
+--R +-+
+--R \|c
+--R +
+--R 3 2 5 2 2 3 2 3
+--R 2b c d x + (18a b c d - 10b c d)x
+--R +
+--R 3 3 2 2 2 2 3 3
+--R (3a d - 9a b c d + 27a b c d - 15b c )x
+--R *
+--R +-+ +-+
+--R \|c \|d
+--R /
+--R 4 2 2 3 +-+ +-+
+--R (6c d x + 6c d )\|c \|d
+--R Type: Expression(Integer)
+--E 101
+
+--S 102 of 994
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R 3 4 2 3 2 2 2 3 3 2 3 3 2 2 2
+--R (3a d + 9a b c d - 27a b c d + 15b c d)x + 3a c d + 9a b c d
+--R +
+--R 2 3 3 4
+--R - 27a b c d + 15b c
+--R *
+--R 2 +-----+
+--R (d x - c)\|- c d + 2c d x
+--R log(---------------------------)
+--R 2
+--R d x + c
+--R +
+--R 3 2 5 2 2 3 2 3
+--R 4b c d x + (36a b c d - 20b c d)x
+--R +
+--R 3 3 2 2 2 2 3 3
+--R (6a d - 18a b c d + 54a b c d - 30b c )x
+--R *
+--R +-----+
+--R \|- c d
+--R /
+--R 4 2 2 3 +-----+
+--R (12c d x + 12c d )\|- c d
+--R ,
+--R
+--R 3 4 2 3 2 2 2 3 3 2 3 3 2 2 2
+--R (3a d + 9a b c d - 27a b c d + 15b c d)x + 3a c d + 9a b c d
+--R +
+--R 2 3 3 4
+--R - 27a b c d + 15b c
+--R *
+--R +---+
+--R x\|c d
+--R atan(-------)
+--R c
+--R +
+--R 3 2 5 2 2 3 2 3
+--R 2b c d x + (18a b c d - 10b c d)x
+--R +
+--R 3 3 2 2 2 2 3 3
+--R (3a d - 9a b c d + 27a b c d - 15b c )x
+--R *
+--R +---+
+--R \|c d
+--R /
+--R 4 2 2 3 +---+
+--R (6c d x + 6c d )\|c d
+--R ]
+--R Type: Union(List(Expression(Integer)),...)
+--E 102
+
+--S 103 of 994
+m0a:=a0.1-r0
+--R
+--R
+--R (4)
+--R 3 3 2 2 2 2 3 3 +-+ +-+
+--R (a d + 3a b c d - 9a b c d + 5b c )\|c \|d
+--R *
+--R 2 +-----+
+--R (d x - c)\|- c d + 2c d x
+--R log(---------------------------)
+--R 2
+--R d x + c
+--R +
+--R +-+
+--R 3 3 2 2 2 2 3 3 +-----+ x\|d
+--R (- 2a d - 6a b c d + 18a b c d - 10b c )\|- c d atan(-----)
+--R +-+
+--R \|c
+--R /
+--R 3 +-----+ +-+ +-+
+--R 4c d \|- c d \|c \|d
+--R Type: Expression(Integer)
+--E 103
+
+--S 104 of 994
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 104
+
+--S 105 of 994
+m0b:=a0.2-r0
+--R
+--R
+--R (6)
+--R +---+
+--R 3 3 2 2 2 2 3 3 +-+ +-+ x\|c d
+--R (a d + 3a b c d - 9a b c d + 5b c )\|c \|d atan(-------)
+--R c
+--R +
+--R +-+
+--R 3 3 2 2 2 2 3 3 +---+ x\|d
+--R (- a d - 3a b c d + 9a b c d - 5b c )\|c d atan(-----)
+--R +-+
+--R \|c
+--R /
+--R 3 +-+ +-+ +---+
+--R 2c d \|c \|d \|c d
+--R Type: Expression(Integer)
+--E 105
+
+--S 106 of 994
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 106
+
+)clear all
+
+--S 107 of 994
+t0:=(a+b*x^2)^3/(c+d*x^2)^3
+--R
+--R
+--R 3 6 2 4 2 2 3
+--R b x + 3a b x + 3a b x + a
+--R (1) -----------------------------
+--R 3 6 2 4 2 2 3
+--R d x + 3c d x + 3c d x + c
+--R Type: Fraction(Polynomial(Integer))
+--E 107
+
+--S 108 of 994
+r0:=b^3*x/d^3-1/4*(b*c-a*d)^3*x/(c*d^3*(c+d*x^2)^2)+3/8*(b*c-a*d)^2*_
+ (3*b*c+a*d)*x/(c^2*d^3*(c+d*x^2))-3/8*(b*c-a*d)*(4*b^2*c^2+_
+ (b*c+a*d)^2)*atan(x*sqrt(d)/sqrt(c))/(c^(5/2)*d^(7/2))
+--R
+--R
+--R (2)
+--R 3 5 2 4 2 2 3 3 3 2 4
+--R (3a d + 3a b c d + 9a b c d - 15b c d )x
+--R +
+--R 3 4 2 2 3 2 3 2 3 4 2 3 2 3 2 3 2
+--R (6a c d + 6a b c d + 18a b c d - 30b c d)x + 3a c d + 3a b c d
+--R +
+--R 2 4 3 5
+--R 9a b c d - 15b c
+--R *
+--R +-+
+--R x\|d
+--R atan(-----)
+--R +-+
+--R \|c
+--R +
+--R 3 2 2 5 3 4 2 3 2 2 2 3 3 3
+--R 8b c d x + (3a d + 3a b c d - 15a b c d + 25b c d)x
+--R +
+--R 3 3 2 2 2 2 3 3 4
+--R (5a c d - 3a b c d - 9a b c d + 15b c )x
+--R *
+--R +-+ +-+
+--R \|c \|d
+--R /
+--R 2 5 4 3 4 2 4 3 +-+ +-+
+--R (8c d x + 16c d x + 8c d )\|c \|d
+--R Type: Expression(Integer)
+--E 108
+
+--S 109 of 994
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R 3 5 2 4 2 2 3 3 3 2 4
+--R (3a d + 3a b c d + 9a b c d - 15b c d )x
+--R +
+--R 3 4 2 2 3 2 3 2 3 4 2 3 2 3
+--R (6a c d + 6a b c d + 18a b c d - 30b c d)x + 3a c d
+--R +
+--R 2 3 2 2 4 3 5
+--R 3a b c d + 9a b c d - 15b c
+--R *
+--R 2 +-----+
+--R (d x - c)\|- c d + 2c d x
+--R log(---------------------------)
+--R 2
+--R d x + c
+--R +
+--R 3 2 2 5 3 4 2 3 2 2 2 3 3 3
+--R 16b c d x + (6a d + 6a b c d - 30a b c d + 50b c d)x
+--R +
+--R 3 3 2 2 2 2 3 3 4
+--R (10a c d - 6a b c d - 18a b c d + 30b c )x
+--R *
+--R +-----+
+--R \|- c d
+--R /
+--R 2 5 4 3 4 2 4 3 +-----+
+--R (16c d x + 32c d x + 16c d )\|- c d
+--R ,
+--R
+--R 3 5 2 4 2 2 3 3 3 2 4
+--R (3a d + 3a b c d + 9a b c d - 15b c d )x
+--R +
+--R 3 4 2 2 3 2 3 2 3 4 2 3 2 3
+--R (6a c d + 6a b c d + 18a b c d - 30b c d)x + 3a c d
+--R +
+--R 2 3 2 2 4 3 5
+--R 3a b c d + 9a b c d - 15b c
+--R *
+--R +---+
+--R x\|c d
+--R atan(-------)
+--R c
+--R +
+--R 3 2 2 5 3 4 2 3 2 2 2 3 3 3
+--R 8b c d x + (3a d + 3a b c d - 15a b c d + 25b c d)x
+--R +
+--R 3 3 2 2 2 2 3 3 4
+--R (5a c d - 3a b c d - 9a b c d + 15b c )x
+--R *
+--R +---+
+--R \|c d
+--R /
+--R 2 5 4 3 4 2 4 3 +---+
+--R (8c d x + 16c d x + 8c d )\|c d
+--R ]
+--R Type: Union(List(Expression(Integer)),...)
+--E 109
+
+--S 110 of 994
+m0a:=a0.1-r0
+--R
+--R
+--R (4)
+--R 3 3 2 2 2 2 3 3 +-+ +-+
+--R (3a d + 3a b c d + 9a b c d - 15b c )\|c \|d
+--R *
+--R 2 +-----+
+--R (d x - c)\|- c d + 2c d x
+--R log(---------------------------)
+--R 2
+--R d x + c
+--R +
+--R +-+
+--R 3 3 2 2 2 2 3 3 +-----+ x\|d
+--R (- 6a d - 6a b c d - 18a b c d + 30b c )\|- c d atan(-----)
+--R +-+
+--R \|c
+--R /
+--R 2 3 +-----+ +-+ +-+
+--R 16c d \|- c d \|c \|d
+--R Type: Expression(Integer)
+--E 110
+
+--S 111 of 994
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 111
+
+--S 112 of 994
+m0b:=a0.2-r0
+--R
+--R
+--R (6)
+--R +---+
+--R 3 3 2 2 2 2 3 3 +-+ +-+ x\|c d
+--R (3a d + 3a b c d + 9a b c d - 15b c )\|c \|d atan(-------)
+--R c
+--R +
+--R +-+
+--R 3 3 2 2 2 2 3 3 +---+ x\|d
+--R (- 3a d - 3a b c d - 9a b c d + 15b c )\|c d atan(-----)
+--R +-+
+--R \|c
+--R /
+--R 2 3 +-+ +-+ +---+
+--R 8c d \|c \|d \|c d
+--R Type: Expression(Integer)
+--E 112
+
+--S 113 of 994
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 113
+
+)clear all
+
+--S 114 of 994
+t0:=(c+d*x^2)^4/(a+b*x^2)
+--R
+--R
+--R 4 8 3 6 2 2 4 3 2 4
+--R d x + 4c d x + 6c d x + 4c d x + c
+--R (1) ---------------------------------------
+--R 2
+--R b x + a
+--R Type: Fraction(Polynomial(Integer))
+--E 114
+
+--S 115 of 994
+r0:=d*(2*b*c-a*d)*(2*b^2*c^2-2*a*b*c*d+a^2*d^2)*x/b^4+1/3*d^2*(6*b^2*c^2-_
+ 4*a*b*c*d+a^2*d^2)*x^3/b^3+1/5*d^3*(4*b*c-a*d)*x^5/b^2+_
+ 1/7*d^4*x^7/b+(b*c-a*d)^4*atan(x*sqrt(b)/sqrt(a))/(b^(9/2)*sqrt(a))
+--R
+--R
+--R (2)
+--R +-+
+--R 4 4 3 3 2 2 2 2 3 3 4 4 x\|b
+--R (105a d - 420a b c d + 630a b c d - 420a b c d + 105b c )atan(-----)
+--R +-+
+--R \|a
+--R +
+--R 3 4 7 2 4 3 3 5
+--R 15b d x + (- 21a b d + 84b c d )x
+--R +
+--R 2 4 2 3 3 2 2 3
+--R (35a b d - 140a b c d + 210b c d )x
+--R +
+--R 3 4 2 3 2 2 2 3 3
+--R (- 105a d + 420a b c d - 630a b c d + 420b c d)x
+--R *
+--R +-+ +-+
+--R \|a \|b
+--R /
+--R 4 +-+ +-+
+--R 105b \|a \|b
+--R Type: Expression(Integer)
+--E 115
+
+--S 116 of 994
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R 4 4 3 3 2 2 2 2 3 3 4 4
+--R (105a d - 420a b c d + 630a b c d - 420a b c d + 105b c )
+--R *
+--R 2 +-----+
+--R (b x - a)\|- a b + 2a b x
+--R log(---------------------------)
+--R 2
+--R b x + a
+--R +
+--R 3 4 7 2 4 3 3 5
+--R 30b d x + (- 42a b d + 168b c d )x
+--R +
+--R 2 4 2 3 3 2 2 3
+--R (70a b d - 280a b c d + 420b c d )x
+--R +
+--R 3 4 2 3 2 2 2 3 3
+--R (- 210a d + 840a b c d - 1260a b c d + 840b c d)x
+--R *
+--R +-----+
+--R \|- a b
+--R /
+--R 4 +-----+
+--R 210b \|- a b
+--R ,
+--R
+--R 4 4 3 3 2 2 2 2 3 3 4 4
+--R (105a d - 420a b c d + 630a b c d - 420a b c d + 105b c )
+--R *
+--R +---+
+--R x\|a b
+--R atan(-------)
+--R a
+--R +
+--R 3 4 7 2 4 3 3 5
+--R 15b d x + (- 21a b d + 84b c d )x
+--R +
+--R 2 4 2 3 3 2 2 3
+--R (35a b d - 140a b c d + 210b c d )x
+--R +
+--R 3 4 2 3 2 2 2 3 3
+--R (- 105a d + 420a b c d - 630a b c d + 420b c d)x
+--R *
+--R +---+
+--R \|a b
+--R /
+--R 4 +---+
+--R 105b \|a b
+--R ]
+--R Type: Union(List(Expression(Integer)),...)
+--E 116
+
+--S 117 of 994
+m0a:=a0.1-r0
+--R
+--R
+--R (4)
+--R 4 4 3 3 2 2 2 2 3 3 4 4 +-+ +-+
+--R (a d - 4a b c d + 6a b c d - 4a b c d + b c )\|a \|b
+--R *
+--R 2 +-----+
+--R (b x - a)\|- a b + 2a b x
+--R log(---------------------------)
+--R 2
+--R b x + a
+--R +
+--R +-+
+--R 4 4 3 3 2 2 2 2 3 3 4 4 +-----+ x\|b
+--R (- 2a d + 8a b c d - 12a b c d + 8a b c d - 2b c )\|- a b atan(-----)
+--R +-+
+--R \|a
+--R /
+--R 4 +-----+ +-+ +-+
+--R 2b \|- a b \|a \|b
+--R Type: Expression(Integer)
+--E 117
+
+--S 118 of 994
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 118
+
+--S 119 of 994
+m0b:=a0.2-r0
+--R
+--R
+--R (6)
+--R +---+
+--R 4 4 3 3 2 2 2 2 3 3 4 4 +-+ +-+ x\|a b
+--R (a d - 4a b c d + 6a b c d - 4a b c d + b c )\|a \|b atan(-------)
+--R a
+--R +
+--R +-+
+--R 4 4 3 3 2 2 2 2 3 3 4 4 +---+ x\|b
+--R (- a d + 4a b c d - 6a b c d + 4a b c d - b c )\|a b atan(-----)
+--R +-+
+--R \|a
+--R /
+--R 4 +-+ +-+ +---+
+--R b \|a \|b \|a b
+--R Type: Expression(Integer)
+--E 119
+
+--S 120 of 994
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 120
+
+)clear all
+
+--S 121 of 994
+t0:=(c+d*x^2)^3/(a+b*x^2)
+--R
+--R
+--R 3 6 2 4 2 2 3
+--R d x + 3c d x + 3c d x + c
+--R (1) -----------------------------
+--R 2
+--R b x + a
+--R Type: Fraction(Polynomial(Integer))
+--E 121
+
+--S 122 of 994
+r0:=d*(3*b^2*c^2-3*a*b*c*d+a^2*d^2)*x/b^3+1/3*d^2*(3*b*c-a*d)*x^3/b^2+_
+ 1/5*d^3*x^5/b+(b*c-a*d)^3*atan(x*sqrt(b)/sqrt(a))/(b^(7/2)*sqrt(a))
+--R
+--R
+--R (2)
+--R +-+
+--R 3 3 2 2 2 2 3 3 x\|b
+--R (- 15a d + 45a b c d - 45a b c d + 15b c )atan(-----)
+--R +-+
+--R \|a
+--R +
+--R 2 3 5 3 2 2 3 2 3 2 2 2
+--R (3b d x + (- 5a b d + 15b c d )x + (15a d - 45a b c d + 45b c d)x)
+--R *
+--R +-+ +-+
+--R \|a \|b
+--R /
+--R 3 +-+ +-+
+--R 15b \|a \|b
+--R Type: Expression(Integer)
+--E 122
+
+--S 123 of 994
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R 3 3 2 2 2 2 3 3
+--R (15a d - 45a b c d + 45a b c d - 15b c )
+--R *
+--R 2 +-----+
+--R (b x - a)\|- a b - 2a b x
+--R log(---------------------------)
+--R 2
+--R b x + a
+--R +
+--R 2 3 5 3 2 2 3
+--R 6b d x + (- 10a b d + 30b c d )x
+--R +
+--R 2 3 2 2 2
+--R (30a d - 90a b c d + 90b c d)x
+--R *
+--R +-----+
+--R \|- a b
+--R /
+--R 3 +-----+
+--R 30b \|- a b
+--R ,
+--R
+--R +---+
+--R 3 3 2 2 2 2 3 3 x\|a b
+--R (- 15a d + 45a b c d - 45a b c d + 15b c )atan(-------)
+--R a
+--R +
+--R 2 3 5 3 2 2 3
+--R 3b d x + (- 5a b d + 15b c d )x
+--R +
+--R 2 3 2 2 2
+--R (15a d - 45a b c d + 45b c d)x
+--R *
+--R +---+
+--R \|a b
+--R /
+--R 3 +---+
+--R 15b \|a b
+--R ]
+--R Type: Union(List(Expression(Integer)),...)
+--E 123
+
+--S 124 of 994
+m0a:=a0.1-r0
+--R
+--R
+--R (4)
+--R 3 3 2 2 2 2 3 3 +-+ +-+
+--R (a d - 3a b c d + 3a b c d - b c )\|a \|b
+--R *
+--R 2 +-----+
+--R (b x - a)\|- a b - 2a b x
+--R log(---------------------------)
+--R 2
+--R b x + a
+--R +
+--R +-+
+--R 3 3 2 2 2 2 3 3 +-----+ x\|b
+--R (2a d - 6a b c d + 6a b c d - 2b c )\|- a b atan(-----)
+--R +-+
+--R \|a
+--R /
+--R 3 +-----+ +-+ +-+
+--R 2b \|- a b \|a \|b
+--R Type: Expression(Integer)
+--E 124
+
+--S 125 of 994
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 125
+
+--S 126 of 994
+m0b:=a0.2-r0
+--R
+--R
+--R (6)
+--R +---+
+--R 3 3 2 2 2 2 3 3 +-+ +-+ x\|a b
+--R (- a d + 3a b c d - 3a b c d + b c )\|a \|b atan(-------)
+--R a
+--R +
+--R +-+
+--R 3 3 2 2 2 2 3 3 +---+ x\|b
+--R (a d - 3a b c d + 3a b c d - b c )\|a b atan(-----)
+--R +-+
+--R \|a
+--R /
+--R 3 +-+ +-+ +---+
+--R b \|a \|b \|a b
+--R Type: Expression(Integer)
+--E 126
+
+--S 127 of 994
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 127
+
+)clear all
+
+--S 128 of 994
+t0:=(c+d*x^2)^2/(a+b*x^2)
+--R
+--R
+--R 2 4 2 2
+--R d x + 2c d x + c
+--R (1) -------------------
+--R 2
+--R b x + a
+--R Type: Fraction(Polynomial(Integer))
+--E 128
+
+--S 129 of 994
+r0:=d*(2*b*c-a*d)*x/b^2+1/3*d^2*x^3/b+(b*c-a*d)^2*atan(x*sqrt(b)/_
+ sqrt(a))/(b^(5/2)*sqrt(a))
+--R
+--R
+--R (2)
+--R +-+
+--R 2 2 2 2 x\|b
+--R (3a d - 6a b c d + 3b c )atan(-----)
+--R +-+
+--R \|a
+--R +
+--R 2 3 2 +-+ +-+
+--R (b d x + (- 3a d + 6b c d)x)\|a \|b
+--R /
+--R 2 +-+ +-+
+--R 3b \|a \|b
+--R Type: Expression(Integer)
+--E 129
+
+--S 130 of 994
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R 2 +-----+
+--R 2 2 2 2 (b x - a)\|- a b + 2a b x
+--R (3a d - 6a b c d + 3b c )log(---------------------------)
+--R 2
+--R b x + a
+--R +
+--R 2 3 2 +-----+
+--R (2b d x + (- 6a d + 12b c d)x)\|- a b
+--R /
+--R 2 +-----+
+--R 6b \|- a b
+--R ,
+--R
+--R +---+
+--R 2 2 2 2 x\|a b
+--R (3a d - 6a b c d + 3b c )atan(-------)
+--R a
+--R +
+--R 2 3 2 +---+
+--R (b d x + (- 3a d + 6b c d)x)\|a b
+--R /
+--R 2 +---+
+--R 3b \|a b
+--R ]
+--R Type: Union(List(Expression(Integer)),...)
+--E 130
+
+--S 131 of 994
+m0a:=a0.1-r0
+--R
+--R
+--R (4)
+--R 2 +-----+
+--R 2 2 2 2 +-+ +-+ (b x - a)\|- a b + 2a b x
+--R (a d - 2a b c d + b c )\|a \|b log(---------------------------)
+--R 2
+--R b x + a
+--R +
+--R +-+
+--R 2 2 2 2 +-----+ x\|b
+--R (- 2a d + 4a b c d - 2b c )\|- a b atan(-----)
+--R +-+
+--R \|a
+--R /
+--R 2 +-----+ +-+ +-+
+--R 2b \|- a b \|a \|b
+--R Type: Expression(Integer)
+--E 131
+
+--S 132 of 994
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 132
+
+--S 133 of 994
+m0b:=a0.2-r0
+--R
+--R
+--R (6)
+--R +---+
+--R 2 2 2 2 +-+ +-+ x\|a b
+--R (a d - 2a b c d + b c )\|a \|b atan(-------)
+--R a
+--R +
+--R +-+
+--R 2 2 2 2 +---+ x\|b
+--R (- a d + 2a b c d - b c )\|a b atan(-----)
+--R +-+
+--R \|a
+--R /
+--R 2 +-+ +-+ +---+
+--R b \|a \|b \|a b
+--R Type: Expression(Integer)
+--E 133
+
+--S 134 of 994
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 134
+
+)clear all
+
+--S 135 of 994
+t0:=(c+d*x^2)/(a+b*x^2)
+--R
+--R
+--R 2
+--R d x + c
+--R (1) --------
+--R 2
+--R b x + a
+--R Type: Fraction(Polynomial(Integer))
+--E 135
+
+--S 136 of 994
+r0:=d*x/b+(b*c-a*d)*atan(x*sqrt(b)/sqrt(a))/(b^(3/2)*sqrt(a))
+--R
+--R
+--R +-+
+--R x\|b +-+ +-+
+--R (- a d + b c)atan(-----) + d x\|a \|b
+--R +-+
+--R \|a
+--R (2) --------------------------------------
+--R +-+ +-+
+--R b\|a \|b
+--R Type: Expression(Integer)
+--E 136
+
+--S 137 of 994
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 2 +-----+
+--R (b x - a)\|- a b - 2a b x +-----+
+--R (a d - b c)log(---------------------------) + 2d x\|- a b
+--R 2
+--R b x + a
+--R [----------------------------------------------------------,
+--R +-----+
+--R 2b\|- a b
+--R +---+
+--R x\|a b +---+
+--R (- a d + b c)atan(-------) + d x\|a b
+--R a
+--R --------------------------------------]
+--R +---+
+--R b\|a b
+--R Type: Union(List(Expression(Integer)),...)
+--E 137
+
+--S 138 of 994
+m0a:=a0.1-r0
+--R
+--R
+--R (4)
+--R 2 +-----+
+--R +-+ +-+ (b x - a)\|- a b - 2a b x
+--R (a d - b c)\|a \|b log(---------------------------)
+--R 2
+--R b x + a
+--R +
+--R +-+
+--R +-----+ x\|b
+--R (2a d - 2b c)\|- a b atan(-----)
+--R +-+
+--R \|a
+--R /
+--R +-----+ +-+ +-+
+--R 2b\|- a b \|a \|b
+--R Type: Expression(Integer)
+--E 138
+
+--S 139 of 994
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 139
+
+--S 140 of 994
+m0b:=a0.2-r0
+--R
+--R
+--R +---+ +-+
+--R +-+ +-+ x\|a b +---+ x\|b
+--R (- a d + b c)\|a \|b atan(-------) + (a d - b c)\|a b atan(-----)
+--R a +-+
+--R \|a
+--R (6) -----------------------------------------------------------------
+--R +-+ +-+ +---+
+--R b\|a \|b \|a b
+--R Type: Expression(Integer)
+--E 140
+
+--S 141 of 994
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 141
+
+)clear all
+
+--S 142 of 994
+t0:=1/((a+b*x^2)*(c+d*x^2))
+--R
+--R
+--R 1
+--R (1) ----------------------------
+--R 4 2
+--R b d x + (a d + b c)x + a c
+--R Type: Fraction(Polynomial(Integer))
+--E 142
+
+--S 143 of 994
+r0:=atan(x*sqrt(b)/sqrt(a))*sqrt(b)/((b*c-a*d)*sqrt(a))-_
+ atan(x*sqrt(d)/sqrt(c))*sqrt(d)/((b*c-a*d)*sqrt(c))
+--R
+--R
+--R +-+ +-+
+--R +-+ +-+ x\|d +-+ +-+ x\|b
+--R \|a \|d atan(-----) - \|b \|c atan(-----)
+--R +-+ +-+
+--R \|c \|a
+--R (2) -----------------------------------------
+--R +-+ +-+
+--R (a d - b c)\|a \|c
+--R Type: Expression(Integer)
+--E 143
+
+--S 144 of 994
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +---+ +---+
+--R | d 2 | b 2
+--R +---+ 2c x |- - + d x - c +---+ - 2a x |- - + b x - a
+--R | d \| c | b \| a
+--R |- - log(---------------------) + |- - log(-----------------------)
+--R \| c 2 \| a 2
+--R d x + c b x + a
+--R [---------------------------------------------------------------------,
+--R 2a d - 2b c
+--R +---+ +-+
+--R | b 2 |d
+--R +---+ - 2a x |- - + b x - a +-+ c |-
+--R | b \| a |d \|c
+--R |- - log(-----------------------) - 2 |- atan(-----)
+--R \| a 2 \|c d x
+--R b x + a
+--R -----------------------------------------------------,
+--R 2a d - 2b c
+--R +---+ +-+
+--R | d 2 |b
+--R +---+ 2c x |- - + d x - c +-+ a |-
+--R | d \| c |b \|a
+--R |- - log(---------------------) + 2 |- atan(-----)
+--R \| c 2 \|a b x
+--R d x + c
+--R ---------------------------------------------------,
+--R 2a d - 2b c
+--R +-+ +-+
+--R |d |b
+--R +-+ c |- +-+ a |-
+--R |d \|c |b \|a
+--R - |- atan(-----) + |- atan(-----)
+--R \|c d x \|a b x
+--R -----------------------------------]
+--R a d - b c
+--R Type: Union(List(Expression(Integer)),...)
+--E 144
+
+--S 145 of 994
+m0a:=a0.1-r0
+--R
+--R
+--R (4)
+--R +---+
+--R | d 2
+--R +---+ 2c x |- - + d x - c
+--R | d +-+ +-+ \| c
+--R |- - \|a \|c log(---------------------)
+--R \| c 2
+--R d x + c
+--R +
+--R +---+
+--R | b 2
+--R +---+ - 2a x |- - + b x - a +-+
+--R | b +-+ +-+ \| a +-+ +-+ x\|d
+--R |- - \|a \|c log(-----------------------) - 2\|a \|d atan(-----)
+--R \| a 2 +-+
+--R b x + a \|c
+--R +
+--R +-+
+--R +-+ +-+ x\|b
+--R 2\|b \|c atan(-----)
+--R +-+
+--R \|a
+--R /
+--R +-+ +-+
+--R (2a d - 2b c)\|a \|c
+--R Type: Expression(Integer)
+--E 145
+
+--S 146 of 994
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 146
+
+--S 147 of 994
+m0b:=a0.2-r0
+--R
+--R
+--R (6)
+--R +---+
+--R | b 2
+--R +---+ - 2a x |- - + b x - a +-+
+--R | b +-+ +-+ \| a +-+ +-+ x\|d
+--R |- - \|a \|c log(-----------------------) - 2\|a \|d atan(-----)
+--R \| a 2 +-+
+--R b x + a \|c
+--R +
+--R +-+
+--R |d
+--R +-+ c |- +-+
+--R +-+ +-+ |d \|c +-+ +-+ x\|b
+--R - 2\|a \|c |- atan(-----) + 2\|b \|c atan(-----)
+--R \|c d x +-+
+--R \|a
+--R /
+--R +-+ +-+
+--R (2a d - 2b c)\|a \|c
+--R Type: Expression(Integer)
+--E 147
+
+--S 148 of 994
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 148
+
+)clear all
+
+--S 149 of 994
+t0:=1/((a+b*x^2)*(c+d*x^2)^2)
+--R
+--R
+--R 1
+--R (1) -----------------------------------------------------
+--R 2 6 2 4 2 2 2
+--R b d x + (a d + 2b c d)x + (2a c d + b c )x + a c
+--R Type: Fraction(Polynomial(Integer))
+--E 149
+
+--S 150 of 994
+r0:=-1/2*d*x/(c*(b*c-a*d)*(c+d*x^2))+b^(3/2)*atan(x*sqrt(b)/sqrt(a))/_
+ ((b*c-a*d)^2*sqrt(a))-1/2*(3*b*c-a*d)*atan(x*sqrt(d)/sqrt(c))*_
+ sqrt(d)/(c^(3/2)*(b*c-a*d)^2)
+--R
+--R
+--R (2)
+--R +-+
+--R 2 2 2 +-+ +-+ x\|d
+--R ((a d - 3b c d)x + a c d - 3b c )\|a \|d atan(-----)
+--R +-+
+--R \|c
+--R +
+--R +-+
+--R 2 2 +-+ +-+ x\|b 2 +-+ +-+
+--R (2b c d x + 2b c )\|b \|c atan(-----) + (a d - b c d)x\|a \|c
+--R +-+
+--R \|a
+--R /
+--R 2 3 2 2 2 3 2 2 2 2 3 2 4 +-+ +-+
+--R ((2a c d - 4a b c d + 2b c d)x + 2a c d - 4a b c d + 2b c )\|a \|c
+--R Type: Expression(Integer)
+--E 150
+
+--S 151 of 994
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R +---+
+--R | b 2
+--R +---+ 2a x |- - + b x - a
+--R 2 2 | b \| a
+--R (2b c d x + 2b c ) |- - log(---------------------)
+--R \| a 2
+--R b x + a
+--R +
+--R +---+
+--R | d 2
+--R +---+ 2c x |- - + d x - c
+--R 2 2 2 | d \| c
+--R ((a d - 3b c d)x + a c d - 3b c ) |- - log(---------------------)
+--R \| c 2
+--R d x + c
+--R +
+--R 2
+--R (2a d - 2b c d)x
+--R /
+--R 2 3 2 2 2 3 2 2 2 2 3 2 4
+--R (4a c d - 8a b c d + 4b c d)x + 4a c d - 8a b c d + 4b c
+--R ,
+--R
+--R +---+
+--R | b 2
+--R +---+ 2a x |- - + b x - a
+--R 2 2 | b \| a
+--R (b c d x + b c ) |- - log(---------------------)
+--R \| a 2
+--R b x + a
+--R +
+--R +-+
+--R |d
+--R +-+ c |-
+--R 2 2 2 |d \|c 2
+--R ((- a d + 3b c d)x - a c d + 3b c ) |- atan(-----) + (a d - b c d)x
+--R \|c d x
+--R /
+--R 2 3 2 2 2 3 2 2 2 2 3 2 4
+--R (2a c d - 4a b c d + 2b c d)x + 2a c d - 4a b c d + 2b c
+--R ,
+--R
+--R +---+
+--R | d 2
+--R +---+ 2c x |- - + d x - c
+--R 2 2 2 | d \| c
+--R ((a d - 3b c d)x + a c d - 3b c ) |- - log(---------------------)
+--R \| c 2
+--R d x + c
+--R +
+--R +-+
+--R |b
+--R +-+ a |-
+--R 2 2 |b \|a 2
+--R (- 4b c d x - 4b c ) |- atan(-----) + (2a d - 2b c d)x
+--R \|a b x
+--R /
+--R 2 3 2 2 2 3 2 2 2 2 3 2 4
+--R (4a c d - 8a b c d + 4b c d)x + 4a c d - 8a b c d + 4b c
+--R ,
+--R
+--R +-+
+--R |d
+--R +-+ c |-
+--R 2 2 2 |d \|c
+--R ((- a d + 3b c d)x - a c d + 3b c ) |- atan(-----)
+--R \|c d x
+--R +
+--R +-+
+--R |b
+--R +-+ a |-
+--R 2 2 |b \|a 2
+--R (- 2b c d x - 2b c ) |- atan(-----) + (a d - b c d)x
+--R \|a b x
+--R /
+--R 2 3 2 2 2 3 2 2 2 2 3 2 4
+--R (2a c d - 4a b c d + 2b c d)x + 2a c d - 4a b c d + 2b c
+--R ]
+--R Type: Union(List(Expression(Integer)),...)
+--E 151
+
+--S 152 of 994
+m0a:=a0.1-r0
+--R
+--R
+--R (4)
+--R +---+
+--R | b 2
+--R +---+ 2a x |- - + b x - a
+--R | b +-+ +-+ \| a
+--R 2b c |- - \|a \|c log(---------------------)
+--R \| a 2
+--R b x + a
+--R +
+--R +---+
+--R | d 2
+--R +---+ 2c x |- - + d x - c
+--R | d +-+ +-+ \| c
+--R (a d - 3b c) |- - \|a \|c log(---------------------)
+--R \| c 2
+--R d x + c
+--R +
+--R +-+ +-+
+--R +-+ +-+ x\|d +-+ +-+ x\|b
+--R (- 2a d + 6b c)\|a \|d atan(-----) - 4b c\|b \|c atan(-----)
+--R +-+ +-+
+--R \|c \|a
+--R /
+--R 2 2 2 2 3 +-+ +-+
+--R (4a c d - 8a b c d + 4b c )\|a \|c
+--R Type: Expression(Integer)
+--E 152
+
+--S 153 of 994
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 153
+
+--S 154 of 994
+m0b:=a0.2-r0
+--R
+--R
+--R (6)
+--R +---+
+--R | b 2
+--R +---+ 2a x |- - + b x - a
+--R | b +-+ +-+ \| a
+--R b c |- - \|a \|c log(---------------------)
+--R \| a 2
+--R b x + a
+--R +
+--R +-+
+--R |d
+--R +-+ +-+ c |-
+--R +-+ +-+ x\|d +-+ +-+ |d \|c
+--R (- a d + 3b c)\|a \|d atan(-----) + (- a d + 3b c)\|a \|c |- atan(-----)
+--R +-+ \|c d x
+--R \|c
+--R +
+--R +-+
+--R +-+ +-+ x\|b
+--R - 2b c\|b \|c atan(-----)
+--R +-+
+--R \|a
+--R /
+--R 2 2 2 2 3 +-+ +-+
+--R (2a c d - 4a b c d + 2b c )\|a \|c
+--R Type: Expression(Integer)
+--E 154
+
+--S 155 of 994
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 155
+
+)clear all
+
+--S 156 of 994
+t0:=1/((a+b*x^2)*(c+d*x^2)^3)
+--R
+--R
+--R (1)
+--R 1
+--R -----------------------------------------------------------------------------
+--R 3 8 3 2 6 2 2 4 2 3 2 3
+--R b d x + (a d + 3b c d )x + (3a c d + 3b c d)x + (3a c d + b c )x + a c
+--R Type: Fraction(Polynomial(Integer))
+--E 156
+
+--S 157 of 994
+r0:=-1/4*d*x/(c*(b*c-a*d)*(c+d*x^2)^2)-1/8*d*(7*b*c-3*a*d)*x/_
+ (c^2*(b*c-a*d)^2*(c+d*x^2))+b^(5/2)*atan(x*sqrt(b)/sqrt(a))/_
+ ((b*c-a*d)^3*sqrt(a))-1/8*(15*b^2*c^2-10*a*b*c*d+3*a^2*d^2)*_
+ atan(x*sqrt(d)/sqrt(c))*sqrt(d)/(c^(5/2)*(b*c-a*d)^3)
+--R
+--R
+--R (2)
+--R 2 4 3 2 2 2 4
+--R (3a d - 10a b c d + 15b c d )x
+--R +
+--R 2 3 2 2 2 3 2 2 2 2 3 2 4
+--R (6a c d - 20a b c d + 30b c d)x + 3a c d - 10a b c d + 15b c
+--R *
+--R +-+
+--R +-+ +-+ x\|d
+--R \|a \|d atan(-----)
+--R +-+
+--R \|c
+--R +
+--R +-+
+--R 2 2 2 4 2 3 2 2 4 +-+ +-+ x\|b
+--R (- 8b c d x - 16b c d x - 8b c )\|b \|c atan(-----)
+--R +-+
+--R \|a
+--R +
+--R 2 4 3 2 2 2 3 2 3 2 2 2 3
+--R ((3a d - 10a b c d + 7b c d )x + (5a c d - 14a b c d + 9b c d)x)
+--R *
+--R +-+ +-+
+--R \|a \|c
+--R /
+--R 3 2 5 2 3 4 2 4 3 3 5 2 4
+--R (8a c d - 24a b c d + 24a b c d - 8b c d )x
+--R +
+--R 3 3 4 2 4 3 2 5 2 3 6 2 3 4 3 2 5 2
+--R (16a c d - 48a b c d + 48a b c d - 16b c d)x + 8a c d - 24a b c d
+--R +
+--R 2 6 3 7
+--R 24a b c d - 8b c
+--R *
+--R +-+ +-+
+--R \|a \|c
+--R Type: Expression(Integer)
+--E 157
+
+--S 158 of 994
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R 2 4 3 2 2 2 4
+--R (3a d - 10a b c d + 15b c d )x
+--R +
+--R 2 3 2 2 2 3 2 2 2 2 3 2 4
+--R (6a c d - 20a b c d + 30b c d)x + 3a c d - 10a b c d + 15b c
+--R *
+--R +---+
+--R | d 2
+--R +---+ 2c x |- - + d x - c
+--R | d \| c
+--R |- - log(---------------------)
+--R \| c 2
+--R d x + c
+--R +
+--R +---+
+--R | b 2
+--R +---+ - 2a x |- - + b x - a
+--R 2 2 2 4 2 3 2 2 4 | b \| a
+--R (8b c d x + 16b c d x + 8b c ) |- - log(-----------------------)
+--R \| a 2
+--R b x + a
+--R +
+--R 2 4 3 2 2 2 3 2 3 2 2 2 3
+--R (6a d - 20a b c d + 14b c d )x + (10a c d - 28a b c d + 18b c d)x
+--R /
+--R 3 2 5 2 3 4 2 4 3 3 5 2 4
+--R (16a c d - 48a b c d + 48a b c d - 16b c d )x
+--R +
+--R 3 3 4 2 4 3 2 5 2 3 6 2 3 4 3
+--R (32a c d - 96a b c d + 96a b c d - 32b c d)x + 16a c d
+--R +
+--R 2 5 2 2 6 3 7
+--R - 48a b c d + 48a b c d - 16b c
+--R ,
+--R
+--R +---+
+--R | b 2
+--R +---+ - 2a x |- - + b x - a
+--R 2 2 2 4 2 3 2 2 4 | b \| a
+--R (4b c d x + 8b c d x + 4b c ) |- - log(-----------------------)
+--R \| a 2
+--R b x + a
+--R +
+--R 2 4 3 2 2 2 4
+--R (- 3a d + 10a b c d - 15b c d )x
+--R +
+--R 2 3 2 2 2 3 2 2 2 2 3 2 4
+--R (- 6a c d + 20a b c d - 30b c d)x - 3a c d + 10a b c d - 15b c
+--R *
+--R +-+
+--R |d
+--R +-+ c |-
+--R |d \|c
+--R |- atan(-----)
+--R \|c d x
+--R +
+--R 2 4 3 2 2 2 3 2 3 2 2 2 3
+--R (3a d - 10a b c d + 7b c d )x + (5a c d - 14a b c d + 9b c d)x
+--R /
+--R 3 2 5 2 3 4 2 4 3 3 5 2 4
+--R (8a c d - 24a b c d + 24a b c d - 8b c d )x
+--R +
+--R 3 3 4 2 4 3 2 5 2 3 6 2 3 4 3 2 5 2
+--R (16a c d - 48a b c d + 48a b c d - 16b c d)x + 8a c d - 24a b c d
+--R +
+--R 2 6 3 7
+--R 24a b c d - 8b c
+--R ,
+--R
+--R 2 4 3 2 2 2 4
+--R (3a d - 10a b c d + 15b c d )x
+--R +
+--R 2 3 2 2 2 3 2 2 2 2 3 2 4
+--R (6a c d - 20a b c d + 30b c d)x + 3a c d - 10a b c d + 15b c
+--R *
+--R +---+
+--R | d 2
+--R +---+ 2c x |- - + d x - c
+--R | d \| c
+--R |- - log(---------------------)
+--R \| c 2
+--R d x + c
+--R +
+--R +-+
+--R |b
+--R +-+ a |-
+--R 2 2 2 4 2 3 2 2 4 |b \|a
+--R (16b c d x + 32b c d x + 16b c ) |- atan(-----)
+--R \|a b x
+--R +
+--R 2 4 3 2 2 2 3 2 3 2 2 2 3
+--R (6a d - 20a b c d + 14b c d )x + (10a c d - 28a b c d + 18b c d)x
+--R /
+--R 3 2 5 2 3 4 2 4 3 3 5 2 4
+--R (16a c d - 48a b c d + 48a b c d - 16b c d )x
+--R +
+--R 3 3 4 2 4 3 2 5 2 3 6 2 3 4 3
+--R (32a c d - 96a b c d + 96a b c d - 32b c d)x + 16a c d
+--R +
+--R 2 5 2 2 6 3 7
+--R - 48a b c d + 48a b c d - 16b c
+--R ,
+--R
+--R 2 4 3 2 2 2 4
+--R (- 3a d + 10a b c d - 15b c d )x
+--R +
+--R 2 3 2 2 2 3 2 2 2 2 3 2 4
+--R (- 6a c d + 20a b c d - 30b c d)x - 3a c d + 10a b c d - 15b c
+--R *
+--R +-+
+--R |d
+--R +-+ c |-
+--R |d \|c
+--R |- atan(-----)
+--R \|c d x
+--R +
+--R +-+
+--R |b
+--R +-+ a |-
+--R 2 2 2 4 2 3 2 2 4 |b \|a
+--R (8b c d x + 16b c d x + 8b c ) |- atan(-----)
+--R \|a b x
+--R +
+--R 2 4 3 2 2 2 3 2 3 2 2 2 3
+--R (3a d - 10a b c d + 7b c d )x + (5a c d - 14a b c d + 9b c d)x
+--R /
+--R 3 2 5 2 3 4 2 4 3 3 5 2 4
+--R (8a c d - 24a b c d + 24a b c d - 8b c d )x
+--R +
+--R 3 3 4 2 4 3 2 5 2 3 6 2 3 4 3 2 5 2
+--R (16a c d - 48a b c d + 48a b c d - 16b c d)x + 8a c d - 24a b c d
+--R +
+--R 2 6 3 7
+--R 24a b c d - 8b c
+--R ]
+--R Type: Union(List(Expression(Integer)),...)
+--E 158
+
+--S 159 of 994
+m0a:=a0.1-r0
+--R
+--R
+--R (4)
+--R +---+
+--R | d 2
+--R +---+ 2c x |- - + d x - c
+--R 2 2 2 2 | d +-+ +-+ \| c
+--R (3a d - 10a b c d + 15b c ) |- - \|a \|c log(---------------------)
+--R \| c 2
+--R d x + c
+--R +
+--R +---+
+--R | b 2
+--R +---+ - 2a x |- - + b x - a
+--R 2 2 | b +-+ +-+ \| a
+--R 8b c |- - \|a \|c log(-----------------------)
+--R \| a 2
+--R b x + a
+--R +
+--R +-+
+--R 2 2 2 2 +-+ +-+ x\|d
+--R (- 6a d + 20a b c d - 30b c )\|a \|d atan(-----)
+--R +-+
+--R \|c
+--R +
+--R +-+
+--R 2 2 +-+ +-+ x\|b
+--R 16b c \|b \|c atan(-----)
+--R +-+
+--R \|a
+--R /
+--R 3 2 3 2 3 2 2 4 3 5 +-+ +-+
+--R (16a c d - 48a b c d + 48a b c d - 16b c )\|a \|c
+--R Type: Expression(Integer)
+--E 159
+
+--S 160 of 994
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 160
+
+--S 161 of 994
+m0b:=a0.2-r0
+--R
+--R
+--R (6)
+--R +---+
+--R | b 2
+--R +---+ - 2a x |- - + b x - a
+--R 2 2 | b +-+ +-+ \| a
+--R 4b c |- - \|a \|c log(-----------------------)
+--R \| a 2
+--R b x + a
+--R +
+--R +-+
+--R 2 2 2 2 +-+ +-+ x\|d
+--R (- 3a d + 10a b c d - 15b c )\|a \|d atan(-----)
+--R +-+
+--R \|c
+--R +
+--R +-+
+--R |d
+--R +-+ c |-
+--R 2 2 2 2 +-+ +-+ |d \|c
+--R (- 3a d + 10a b c d - 15b c )\|a \|c |- atan(-----)
+--R \|c d x
+--R +
+--R +-+
+--R 2 2 +-+ +-+ x\|b
+--R 8b c \|b \|c atan(-----)
+--R +-+
+--R \|a
+--R /
+--R 3 2 3 2 3 2 2 4 3 5 +-+ +-+
+--R (8a c d - 24a b c d + 24a b c d - 8b c )\|a \|c
+--R Type: Expression(Integer)
+--E 161
+
+--S 162 of 994
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 162
+
+)clear all
+
+--S 163 of 994
+t0:=(c+d*x^2)^5/(a+b*x^2)^2
+--R
+--R
+--R 5 10 4 8 2 3 6 3 2 4 4 2 5
+--R d x + 5c d x + 10c d x + 10c d x + 5c d x + c
+--R (1) ----------------------------------------------------
+--R 2 4 2 2
+--R b x + 2a b x + a
+--R Type: Fraction(Polynomial(Integer))
+--E 163
+
+--S 164 of 994
+r0:=d^2*(10*b^3*c^3-20*a*b^2*c^2*d+15*a^2*b*c*d^2-4*a^3*d^3)*x/b^5+_
+ 1/3*d^3*(10*b^2*c^2-10*a*b*c*d+3*a^2*d^2)*x^3/b^4+1/5*d^4*_
+ (5*b*c-2*a*d)*x^5/b^3+1/7*d^5*x^7/b^2+1/2*(b*c-a*d)^5*x/_
+ (a*b^5*(a+b*x^2))+1/2*(b*c-a*d)^4*(b*c+9*a*d)*atan(x*sqrt(b)/_
+ sqrt(a))/(a^(3/2)*b^(11/2))
+--R
+--R
+--R (2)
+--R 5 5 4 2 4 3 3 2 3 2 4 3 2
+--R 945a b d - 3675a b c d + 5250a b c d - 3150a b c d
+--R +
+--R 5 4 6 5
+--R 525a b c d + 105b c
+--R *
+--R 2
+--R x
+--R +
+--R 6 5 5 4 4 2 2 3 3 3 3 2 2 4 4
+--R 945a d - 3675a b c d + 5250a b c d - 3150a b c d + 525a b c d
+--R +
+--R 5 5
+--R 105a b c
+--R *
+--R +-+
+--R x\|b
+--R atan(-----)
+--R +-+
+--R \|a
+--R +
+--R 4 5 9 2 3 5 4 4 7
+--R 30a b d x + (- 54a b d + 210a b c d )x
+--R +
+--R 3 2 5 2 3 4 4 2 3 5
+--R (126a b d - 490a b c d + 700a b c d )x
+--R +
+--R 4 5 3 2 4 2 3 2 3 4 3 2 3
+--R (- 630a b d + 2450a b c d - 3500a b c d + 2100a b c d )x
+--R +
+--R 5 5 4 4 3 2 2 3 2 3 3 2
+--R - 945a d + 3675a b c d - 5250a b c d + 3150a b c d
+--R +
+--R 4 4 5 5
+--R - 525a b c d + 105b c
+--R *
+--R x
+--R *
+--R +-+ +-+
+--R \|a \|b
+--R /
+--R 6 2 2 5 +-+ +-+
+--R (210a b x + 210a b )\|a \|b
+--R Type: Expression(Integer)
+--E 164
+
+--S 165 of 994
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R 5 5 4 2 4 3 3 2 3 2 4 3 2
+--R 945a b d - 3675a b c d + 5250a b c d - 3150a b c d
+--R +
+--R 5 4 6 5
+--R 525a b c d + 105b c
+--R *
+--R 2
+--R x
+--R +
+--R 6 5 5 4 4 2 2 3 3 3 3 2 2 4 4
+--R 945a d - 3675a b c d + 5250a b c d - 3150a b c d + 525a b c d
+--R +
+--R 5 5
+--R 105a b c
+--R *
+--R 2 +-----+
+--R (b x - a)\|- a b + 2a b x
+--R log(---------------------------)
+--R 2
+--R b x + a
+--R +
+--R 4 5 9 2 3 5 4 4 7
+--R 60a b d x + (- 108a b d + 420a b c d )x
+--R +
+--R 3 2 5 2 3 4 4 2 3 5
+--R (252a b d - 980a b c d + 1400a b c d )x
+--R +
+--R 4 5 3 2 4 2 3 2 3 4 3 2 3
+--R (- 1260a b d + 4900a b c d - 7000a b c d + 4200a b c d )x
+--R +
+--R 5 5 4 4 3 2 2 3 2 3 3 2
+--R - 1890a d + 7350a b c d - 10500a b c d + 6300a b c d
+--R +
+--R 4 4 5 5
+--R - 1050a b c d + 210b c
+--R *
+--R x
+--R *
+--R +-----+
+--R \|- a b
+--R /
+--R 6 2 2 5 +-----+
+--R (420a b x + 420a b )\|- a b
+--R ,
+--R
+--R 5 5 4 2 4 3 3 2 3 2 4 3 2
+--R 945a b d - 3675a b c d + 5250a b c d - 3150a b c d
+--R +
+--R 5 4 6 5
+--R 525a b c d + 105b c
+--R *
+--R 2
+--R x
+--R +
+--R 6 5 5 4 4 2 2 3 3 3 3 2 2 4 4
+--R 945a d - 3675a b c d + 5250a b c d - 3150a b c d + 525a b c d
+--R +
+--R 5 5
+--R 105a b c
+--R *
+--R +---+
+--R x\|a b
+--R atan(-------)
+--R a
+--R +
+--R 4 5 9 2 3 5 4 4 7
+--R 30a b d x + (- 54a b d + 210a b c d )x
+--R +
+--R 3 2 5 2 3 4 4 2 3 5
+--R (126a b d - 490a b c d + 700a b c d )x
+--R +
+--R 4 5 3 2 4 2 3 2 3 4 3 2 3
+--R (- 630a b d + 2450a b c d - 3500a b c d + 2100a b c d )x
+--R +
+--R 5 5 4 4 3 2 2 3 2 3 3 2
+--R - 945a d + 3675a b c d - 5250a b c d + 3150a b c d
+--R +
+--R 4 4 5 5
+--R - 525a b c d + 105b c
+--R *
+--R x
+--R *
+--R +---+
+--R \|a b
+--R /
+--R 6 2 2 5 +---+
+--R (210a b x + 210a b )\|a b
+--R ]
+--R Type: Union(List(Expression(Integer)),...)
+--E 165
+
+--S 166 of 994
+m0a:=a0.1-r0
+--R
+--R
+--R (4)
+--R 5 5 4 4 3 2 2 3 2 3 3 2 4 4 5 5 +-+
+--R (9a d - 35a b c d + 50a b c d - 30a b c d + 5a b c d + b c )\|a
+--R *
+--R 2 +-----+
+--R +-+ (b x - a)\|- a b + 2a b x
+--R \|b log(---------------------------)
+--R 2
+--R b x + a
+--R +
+--R 5 5 4 4 3 2 2 3 2 3 3 2 4 4 5 5
+--R (- 18a d + 70a b c d - 100a b c d + 60a b c d - 10a b c d - 2b c )
+--R *
+--R +-+
+--R +-----+ x\|b
+--R \|- a b atan(-----)
+--R +-+
+--R \|a
+--R /
+--R 5 +-----+ +-+ +-+
+--R 4a b \|- a b \|a \|b
+--R Type: Expression(Integer)
+--E 166
+
+--S 167 of 994
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 167
+
+--S 168 of 994
+m0b:=a0.2-r0
+--R
+--R
+--R (6)
+--R 5 5 4 4 3 2 2 3 2 3 3 2 4 4 5 5 +-+
+--R (9a d - 35a b c d + 50a b c d - 30a b c d + 5a b c d + b c )\|a
+--R *
+--R +---+
+--R +-+ x\|a b
+--R \|b atan(-------)
+--R a
+--R +
+--R 5 5 4 4 3 2 2 3 2 3 3 2 4 4 5 5
+--R (- 9a d + 35a b c d - 50a b c d + 30a b c d - 5a b c d - b c )
+--R *
+--R +-+
+--R +---+ x\|b
+--R \|a b atan(-----)
+--R +-+
+--R \|a
+--R /
+--R 5 +-+ +-+ +---+
+--R 2a b \|a \|b \|a b
+--R Type: Expression(Integer)
+--E 168
+
+--S 169 of 994
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 169
+
+)clear all
+
+--S 170 of 994
+t0:=(c+d*x^2)^4/(a+b*x^2)^2
+--R
+--R
+--R 4 8 3 6 2 2 4 3 2 4
+--R d x + 4c d x + 6c d x + 4c d x + c
+--R (1) ---------------------------------------
+--R 2 4 2 2
+--R b x + 2a b x + a
+--R Type: Fraction(Polynomial(Integer))
+--E 170
+
+--S 171 of 994
+r0:=d^2*(6*b^2*c^2-8*a*b*c*d+3*a^2*d^2)*x/b^4+2/3*d^3*(2*b*c-a*d)*_
+ x^3/b^3+1/5*d^4*x^5/b^2+1/2*(b*c-a*d)^4*x/(a*b^4*(a+b*x^2))+_
+ 1/2*(b*c-a*d)^3*(b*c+7*a*d)*atan(x*sqrt(b)/sqrt(a))/(a^(3/2)*b^(9/2))
+--R
+--R
+--R (2)
+--R 4 4 3 2 3 2 3 2 2 4 3 5 4 2
+--R (- 105a b d + 300a b c d - 270a b c d + 60a b c d + 15b c )x
+--R +
+--R 5 4 4 3 3 2 2 2 2 3 3 4 4
+--R - 105a d + 300a b c d - 270a b c d + 60a b c d + 15a b c
+--R *
+--R +-+
+--R x\|b
+--R atan(-----)
+--R +-+
+--R \|a
+--R +
+--R 3 4 7 2 2 4 3 3 5
+--R 6a b d x + (- 14a b d + 40a b c d )x
+--R +
+--R 3 4 2 2 3 3 2 2 3
+--R (70a b d - 200a b c d + 180a b c d )x
+--R +
+--R 4 4 3 3 2 2 2 2 3 3 4 4
+--R (105a d - 300a b c d + 270a b c d - 60a b c d + 15b c )x
+--R *
+--R +-+ +-+
+--R \|a \|b
+--R /
+--R 5 2 2 4 +-+ +-+
+--R (30a b x + 30a b )\|a \|b
+--R Type: Expression(Integer)
+--E 171
+
+--S 172 of 994
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R 4 4 3 2 3 2 3 2 2 4 3 5 4 2
+--R (105a b d - 300a b c d + 270a b c d - 60a b c d - 15b c )x
+--R +
+--R 5 4 4 3 3 2 2 2 2 3 3 4 4
+--R 105a d - 300a b c d + 270a b c d - 60a b c d - 15a b c
+--R *
+--R 2 +-----+
+--R (b x - a)\|- a b - 2a b x
+--R log(---------------------------)
+--R 2
+--R b x + a
+--R +
+--R 3 4 7 2 2 4 3 3 5
+--R 12a b d x + (- 28a b d + 80a b c d )x
+--R +
+--R 3 4 2 2 3 3 2 2 3
+--R (140a b d - 400a b c d + 360a b c d )x
+--R +
+--R 4 4 3 3 2 2 2 2 3 3 4 4
+--R (210a d - 600a b c d + 540a b c d - 120a b c d + 30b c )x
+--R *
+--R +-----+
+--R \|- a b
+--R /
+--R 5 2 2 4 +-----+
+--R (60a b x + 60a b )\|- a b
+--R ,
+--R
+--R 4 4 3 2 3 2 3 2 2 4 3 5 4 2
+--R (- 105a b d + 300a b c d - 270a b c d + 60a b c d + 15b c )x
+--R +
+--R 5 4 4 3 3 2 2 2 2 3 3 4 4
+--R - 105a d + 300a b c d - 270a b c d + 60a b c d + 15a b c
+--R *
+--R +---+
+--R x\|a b
+--R atan(-------)
+--R a
+--R +
+--R 3 4 7 2 2 4 3 3 5
+--R 6a b d x + (- 14a b d + 40a b c d )x
+--R +
+--R 3 4 2 2 3 3 2 2 3
+--R (70a b d - 200a b c d + 180a b c d )x
+--R +
+--R 4 4 3 3 2 2 2 2 3 3 4 4
+--R (105a d - 300a b c d + 270a b c d - 60a b c d + 15b c )x
+--R *
+--R +---+
+--R \|a b
+--R /
+--R 5 2 2 4 +---+
+--R (30a b x + 30a b )\|a b
+--R ]
+--R Type: Union(List(Expression(Integer)),...)
+--E 172
+
+--S 173 of 994
+m0a:=a0.1-r0
+--R
+--R
+--R (4)
+--R 4 4 3 3 2 2 2 2 3 3 4 4 +-+ +-+
+--R (7a d - 20a b c d + 18a b c d - 4a b c d - b c )\|a \|b
+--R *
+--R 2 +-----+
+--R (b x - a)\|- a b - 2a b x
+--R log(---------------------------)
+--R 2
+--R b x + a
+--R +
+--R +-+
+--R 4 4 3 3 2 2 2 2 3 3 4 4 +-----+ x\|b
+--R (14a d - 40a b c d + 36a b c d - 8a b c d - 2b c )\|- a b atan(-----)
+--R +-+
+--R \|a
+--R /
+--R 4 +-----+ +-+ +-+
+--R 4a b \|- a b \|a \|b
+--R Type: Expression(Integer)
+--E 173
+
+--S 174 of 994
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 174
+
+--S 175 of 994
+m0b:=a0.2-r0
+--R
+--R
+--R (6)
+--R 4 4 3 3 2 2 2 2 3 3 4 4 +-+ +-+
+--R (- 7a d + 20a b c d - 18a b c d + 4a b c d + b c )\|a \|b
+--R *
+--R +---+
+--R x\|a b
+--R atan(-------)
+--R a
+--R +
+--R +-+
+--R 4 4 3 3 2 2 2 2 3 3 4 4 +---+ x\|b
+--R (7a d - 20a b c d + 18a b c d - 4a b c d - b c )\|a b atan(-----)
+--R +-+
+--R \|a
+--R /
+--R 4 +-+ +-+ +---+
+--R 2a b \|a \|b \|a b
+--R Type: Expression(Integer)
+--E 175
+
+--S 176 of 994
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 176
+
+)clear all
+
+--S 177 of 994
+t0:=(c+d*x^2)^3/(a+b*x^2)^2
+--R
+--R
+--R 3 6 2 4 2 2 3
+--R d x + 3c d x + 3c d x + c
+--R (1) -----------------------------
+--R 2 4 2 2
+--R b x + 2a b x + a
+--R Type: Fraction(Polynomial(Integer))
+--E 177
+
+--S 178 of 994
+r0:=d^2*(3*b*c-2*a*d)*x/b^3+1/3*d^3*x^3/b^2+1/2*(b*c-a*d)^3*x/_
+ (a*b^3*(a+b*x^2))+1/2*(b*c-a*d)^2*(b*c+5*a*d)*atan(x*sqrt(b)/_
+ sqrt(a))/(a^(3/2)*b^(7/2))
+--R
+--R
+--R (2)
+--R 3 3 2 2 2 3 2 4 3 2 4 3 3 2
+--R (15a b d - 27a b c d + 9a b c d + 3b c )x + 15a d - 27a b c d
+--R +
+--R 2 2 2 3 3
+--R 9a b c d + 3a b c
+--R *
+--R +-+
+--R x\|b
+--R atan(-----)
+--R +-+
+--R \|a
+--R +
+--R 2 3 5 2 3 2 2 3
+--R 2a b d x + (- 10a b d + 18a b c d )x
+--R +
+--R 3 3 2 2 2 2 3 3
+--R (- 15a d + 27a b c d - 9a b c d + 3b c )x
+--R *
+--R +-+ +-+
+--R \|a \|b
+--R /
+--R 4 2 2 3 +-+ +-+
+--R (6a b x + 6a b )\|a \|b
+--R Type: Expression(Integer)
+--E 178
+
+--S 179 of 994
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R 3 3 2 2 2 3 2 4 3 2 4 3 3 2
+--R (15a b d - 27a b c d + 9a b c d + 3b c )x + 15a d - 27a b c d
+--R +
+--R 2 2 2 3 3
+--R 9a b c d + 3a b c
+--R *
+--R 2 +-----+
+--R (b x - a)\|- a b + 2a b x
+--R log(---------------------------)
+--R 2
+--R b x + a
+--R +
+--R 2 3 5 2 3 2 2 3
+--R 4a b d x + (- 20a b d + 36a b c d )x
+--R +
+--R 3 3 2 2 2 2 3 3
+--R (- 30a d + 54a b c d - 18a b c d + 6b c )x
+--R *
+--R +-----+
+--R \|- a b
+--R /
+--R 4 2 2 3 +-----+
+--R (12a b x + 12a b )\|- a b
+--R ,
+--R
+--R 3 3 2 2 2 3 2 4 3 2 4 3 3 2
+--R (15a b d - 27a b c d + 9a b c d + 3b c )x + 15a d - 27a b c d
+--R +
+--R 2 2 2 3 3
+--R 9a b c d + 3a b c
+--R *
+--R +---+
+--R x\|a b
+--R atan(-------)
+--R a
+--R +
+--R 2 3 5 2 3 2 2 3
+--R 2a b d x + (- 10a b d + 18a b c d )x
+--R +
+--R 3 3 2 2 2 2 3 3
+--R (- 15a d + 27a b c d - 9a b c d + 3b c )x
+--R *
+--R +---+
+--R \|a b
+--R /
+--R 4 2 2 3 +---+
+--R (6a b x + 6a b )\|a b
+--R ]
+--R Type: Union(List(Expression(Integer)),...)
+--E 179
+
+--S 180 of 994
+m0a:=a0.1-r0
+--R
+--R
+--R (4)
+--R 3 3 2 2 2 2 3 3 +-+ +-+
+--R (5a d - 9a b c d + 3a b c d + b c )\|a \|b
+--R *
+--R 2 +-----+
+--R (b x - a)\|- a b + 2a b x
+--R log(---------------------------)
+--R 2
+--R b x + a
+--R +
+--R +-+
+--R 3 3 2 2 2 2 3 3 +-----+ x\|b
+--R (- 10a d + 18a b c d - 6a b c d - 2b c )\|- a b atan(-----)
+--R +-+
+--R \|a
+--R /
+--R 3 +-----+ +-+ +-+
+--R 4a b \|- a b \|a \|b
+--R Type: Expression(Integer)
+--E 180
+
+--S 181 of 994
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 181
+
+--S 182 of 994
+m0b:=a0.2-r0
+--R
+--R
+--R (6)
+--R +---+
+--R 3 3 2 2 2 2 3 3 +-+ +-+ x\|a b
+--R (5a d - 9a b c d + 3a b c d + b c )\|a \|b atan(-------)
+--R a
+--R +
+--R +-+
+--R 3 3 2 2 2 2 3 3 +---+ x\|b
+--R (- 5a d + 9a b c d - 3a b c d - b c )\|a b atan(-----)
+--R +-+
+--R \|a
+--R /
+--R 3 +-+ +-+ +---+
+--R 2a b \|a \|b \|a b
+--R Type: Expression(Integer)
+--E 182
+
+--S 183 of 994
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 183
+
+)clear all
+
+--S 184 of 994
+t0:=(c+d*x^2)^2/(a+b*x^2)^2
+--R
+--R
+--R 2 4 2 2
+--R d x + 2c d x + c
+--R (1) -------------------
+--R 2 4 2 2
+--R b x + 2a b x + a
+--R Type: Fraction(Polynomial(Integer))
+--E 184
+
+--S 185 of 994
+r0:=d^2*x/b^2+1/2*(b*c-a*d)^2*x/(a*b^2*(a+b*x^2))+1/2*(b*c-a*d)*_
+ (b*c+3*a*d)*atan(x*sqrt(b)/sqrt(a))/(a^(3/2)*b^(5/2))
+--R
+--R
+--R (2)
+--R +-+
+--R 2 2 2 3 2 2 3 2 2 2 2 x\|b
+--R ((- 3a b d + 2a b c d + b c )x - 3a d + 2a b c d + a b c )atan(-----)
+--R +-+
+--R \|a
+--R +
+--R 2 3 2 2 2 2 +-+ +-+
+--R (2a b d x + (3a d - 2a b c d + b c )x)\|a \|b
+--R /
+--R 3 2 2 2 +-+ +-+
+--R (2a b x + 2a b )\|a \|b
+--R Type: Expression(Integer)
+--E 185
+
+--S 186 of 994
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R 2 2 2 3 2 2 3 2 2 2 2
+--R ((3a b d - 2a b c d - b c )x + 3a d - 2a b c d - a b c )
+--R *
+--R 2 +-----+
+--R (b x - a)\|- a b - 2a b x
+--R log(---------------------------)
+--R 2
+--R b x + a
+--R +
+--R 2 3 2 2 2 2 +-----+
+--R (4a b d x + (6a d - 4a b c d + 2b c )x)\|- a b
+--R /
+--R 3 2 2 2 +-----+
+--R (4a b x + 4a b )\|- a b
+--R ,
+--R
+--R 2 2 2 3 2 2 3 2 2 2 2
+--R ((- 3a b d + 2a b c d + b c )x - 3a d + 2a b c d + a b c )
+--R *
+--R +---+
+--R x\|a b
+--R atan(-------)
+--R a
+--R +
+--R 2 3 2 2 2 2 +---+
+--R (2a b d x + (3a d - 2a b c d + b c )x)\|a b
+--R /
+--R 3 2 2 2 +---+
+--R (2a b x + 2a b )\|a b
+--R ]
+--R Type: Union(List(Expression(Integer)),...)
+--E 186
+
+--S 187 of 994
+m0a:=a0.1-r0
+--R
+--R
+--R (4)
+--R 2 +-----+
+--R 2 2 2 2 +-+ +-+ (b x - a)\|- a b - 2a b x
+--R (3a d - 2a b c d - b c )\|a \|b log(---------------------------)
+--R 2
+--R b x + a
+--R +
+--R +-+
+--R 2 2 2 2 +-----+ x\|b
+--R (6a d - 4a b c d - 2b c )\|- a b atan(-----)
+--R +-+
+--R \|a
+--R /
+--R 2 +-----+ +-+ +-+
+--R 4a b \|- a b \|a \|b
+--R Type: Expression(Integer)
+--E 187
+
+--S 188 of 994
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 188
+
+--S 189 of 994
+m0b:=a0.2-r0
+--R
+--R
+--R (6)
+--R +---+
+--R 2 2 2 2 +-+ +-+ x\|a b
+--R (- 3a d + 2a b c d + b c )\|a \|b atan(-------)
+--R a
+--R +
+--R +-+
+--R 2 2 2 2 +---+ x\|b
+--R (3a d - 2a b c d - b c )\|a b atan(-----)
+--R +-+
+--R \|a
+--R /
+--R 2 +-+ +-+ +---+
+--R 2a b \|a \|b \|a b
+--R Type: Expression(Integer)
+--E 189
+
+--S 190 of 994
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 190
+
+)clear all
+
+--S 191 of 994
+t0:=(c+d*x^2)/(a+b*x^2)^2
+--R
+--R
+--R 2
+--R d x + c
+--R (1) -------------------
+--R 2 4 2 2
+--R b x + 2a b x + a
+--R Type: Fraction(Polynomial(Integer))
+--E 191
+
+--S 192 of 994
+r0:=1/2*(b*c-a*d)*x/(a*b*(a+b*x^2))+1/2*(b*c+a*d)*atan(x*sqrt(b)/_
+ sqrt(a))/(a^(3/2)*b^(3/2))
+--R
+--R
+--R +-+
+--R 2 2 2 x\|b +-+ +-+
+--R ((a b d + b c)x + a d + a b c)atan(-----) + (- a d + b c)x\|a \|b
+--R +-+
+--R \|a
+--R (2) -------------------------------------------------------------------
+--R 2 2 2 +-+ +-+
+--R (2a b x + 2a b)\|a \|b
+--R Type: Expression(Integer)
+--E 192
+
+--S 193 of 994
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R 2 +-----+
+--R 2 2 2 (b x - a)\|- a b + 2a b x
+--R ((a b d + b c)x + a d + a b c)log(---------------------------)
+--R 2
+--R b x + a
+--R +
+--R +-----+
+--R (- 2a d + 2b c)x\|- a b
+--R /
+--R 2 2 2 +-----+
+--R (4a b x + 4a b)\|- a b
+--R ,
+--R +---+
+--R 2 2 2 x\|a b +---+
+--R ((a b d + b c)x + a d + a b c)atan(-------) + (- a d + b c)x\|a b
+--R a
+--R -------------------------------------------------------------------]
+--R 2 2 2 +---+
+--R (2a b x + 2a b)\|a b
+--R Type: Union(List(Expression(Integer)),...)
+--E 193
+
+--S 194 of 994
+m0a:=a0.1-r0
+--R
+--R
+--R (4)
+--R 2 +-----+
+--R +-+ +-+ (b x - a)\|- a b + 2a b x
+--R (a d + b c)\|a \|b log(---------------------------)
+--R 2
+--R b x + a
+--R +
+--R +-+
+--R +-----+ x\|b
+--R (- 2a d - 2b c)\|- a b atan(-----)
+--R +-+
+--R \|a
+--R /
+--R +-----+ +-+ +-+
+--R 4a b\|- a b \|a \|b
+--R Type: Expression(Integer)
+--E 194
+
+--S 195 of 994
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 195
+
+--S 196 of 994
+m0b:=a0.2-r0
+--R
+--R
+--R +---+ +-+
+--R +-+ +-+ x\|a b +---+ x\|b
+--R (a d + b c)\|a \|b atan(-------) + (- a d - b c)\|a b atan(-----)
+--R a +-+
+--R \|a
+--R (6) -----------------------------------------------------------------
+--R +-+ +-+ +---+
+--R 2a b\|a \|b \|a b
+--R Type: Expression(Integer)
+--E 196
+
+--S 197 of 994
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 197
+
+)clear all
+
+--S 198 of 994
+t0:=1/((a+b*x^2)^2*(c+d*x^2))
+--R
+--R
+--R 1
+--R (1) --------------------------------------------------
+--R 2 6 2 4 2 2 2
+--R b d x + (2a b d + b c)x + (a d + 2a b c)x + a c
+--R Type: Fraction(Polynomial(Integer))
+--E 198
+
+--S 199 of 994
+r0:=1/2*b*x/(a*(b*c-a*d)*(a+b*x^2))+1/2*(b*c-3*a*d)*atan(x*sqrt(b)/_
+ sqrt(a))*sqrt(b)/(a^(3/2)*(b*c-a*d)^2)+d^(3/2)*atan(x*sqrt(d)/_
+ sqrt(c))/((b*c-a*d)^2*sqrt(c))
+--R
+--R
+--R (2)
+--R +-+
+--R 2 2 +-+ +-+ x\|d
+--R (2a b d x + 2a d)\|a \|d atan(-----)
+--R +-+
+--R \|c
+--R +
+--R +-+
+--R 2 2 2 +-+ +-+ x\|b
+--R ((- 3a b d + b c)x - 3a d + a b c)\|b \|c atan(-----)
+--R +-+
+--R \|a
+--R +
+--R 2 +-+ +-+
+--R (- a b d + b c)x\|a \|c
+--R /
+--R 3 2 2 2 3 2 2 4 2 3 2 2 2 +-+ +-+
+--R ((2a b d - 4a b c d + 2a b c )x + 2a d - 4a b c d + 2a b c )\|a \|c
+--R Type: Expression(Integer)
+--E 199
+
+--S 200 of 994
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R +---+
+--R | d 2
+--R +---+ 2c x |- - + d x - c
+--R 2 2 | d \| c
+--R (2a b d x + 2a d) |- - log(---------------------)
+--R \| c 2
+--R d x + c
+--R +
+--R +---+
+--R | b 2
+--R +---+ - 2a x |- - + b x - a
+--R 2 2 2 | b \| a
+--R ((3a b d - b c)x + 3a d - a b c) |- - log(-----------------------)
+--R \| a 2
+--R b x + a
+--R +
+--R 2
+--R (- 2a b d + 2b c)x
+--R /
+--R 3 2 2 2 3 2 2 4 2 3 2 2 2
+--R (4a b d - 8a b c d + 4a b c )x + 4a d - 8a b c d + 4a b c
+--R ,
+--R
+--R +---+
+--R | b 2
+--R +---+ - 2a x |- - + b x - a
+--R 2 2 2 | b \| a
+--R ((3a b d - b c)x + 3a d - a b c) |- - log(-----------------------)
+--R \| a 2
+--R b x + a
+--R +
+--R +-+
+--R |d
+--R +-+ c |-
+--R 2 2 |d \|c 2
+--R (- 4a b d x - 4a d) |- atan(-----) + (- 2a b d + 2b c)x
+--R \|c d x
+--R /
+--R 3 2 2 2 3 2 2 4 2 3 2 2 2
+--R (4a b d - 8a b c d + 4a b c )x + 4a d - 8a b c d + 4a b c
+--R ,
+--R
+--R +---+
+--R | d 2
+--R +---+ 2c x |- - + d x - c
+--R 2 2 | d \| c
+--R (a b d x + a d) |- - log(---------------------)
+--R \| c 2
+--R d x + c
+--R +
+--R +-+
+--R |b
+--R +-+ a |-
+--R 2 2 2 |b \|a 2
+--R ((3a b d - b c)x + 3a d - a b c) |- atan(-----) + (- a b d + b c)x
+--R \|a b x
+--R /
+--R 3 2 2 2 3 2 2 4 2 3 2 2 2
+--R (2a b d - 4a b c d + 2a b c )x + 2a d - 4a b c d + 2a b c
+--R ,
+--R
+--R +-+
+--R |d
+--R +-+ c |-
+--R 2 2 |d \|c
+--R (- 2a b d x - 2a d) |- atan(-----)
+--R \|c d x
+--R +
+--R +-+
+--R |b
+--R +-+ a |-
+--R 2 2 2 |b \|a 2
+--R ((3a b d - b c)x + 3a d - a b c) |- atan(-----) + (- a b d + b c)x
+--R \|a b x
+--R /
+--R 3 2 2 2 3 2 2 4 2 3 2 2 2
+--R (2a b d - 4a b c d + 2a b c )x + 2a d - 4a b c d + 2a b c
+--R ]
+--R Type: Union(List(Expression(Integer)),...)
+--E 200
+
+--S 201 of 994
+m0a:=a0.1-r0
+--R
+--R
+--R (4)
+--R +---+
+--R | d 2
+--R +---+ 2c x |- - + d x - c
+--R | d +-+ +-+ \| c
+--R 2a d |- - \|a \|c log(---------------------)
+--R \| c 2
+--R d x + c
+--R +
+--R +---+
+--R | b 2
+--R +---+ - 2a x |- - + b x - a
+--R | b +-+ +-+ \| a
+--R (3a d - b c) |- - \|a \|c log(-----------------------)
+--R \| a 2
+--R b x + a
+--R +
+--R +-+ +-+
+--R +-+ +-+ x\|d +-+ +-+ x\|b
+--R - 4a d\|a \|d atan(-----) + (6a d - 2b c)\|b \|c atan(-----)
+--R +-+ +-+
+--R \|c \|a
+--R /
+--R 3 2 2 2 2 +-+ +-+
+--R (4a d - 8a b c d + 4a b c )\|a \|c
+--R Type: Expression(Integer)
+--E 201
+
+--S 202 of 994
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 202
+
+--S 203 of 994
+m0b:=a0.2-r0
+--R
+--R
+--R (6)
+--R +---+
+--R | b 2
+--R +---+ - 2a x |- - + b x - a
+--R | b +-+ +-+ \| a
+--R (3a d - b c) |- - \|a \|c log(-----------------------)
+--R \| a 2
+--R b x + a
+--R +
+--R +-+
+--R |d
+--R +-+ +-+ c |-
+--R +-+ +-+ x\|d +-+ +-+ |d \|c
+--R - 4a d\|a \|d atan(-----) - 4a d\|a \|c |- atan(-----)
+--R +-+ \|c d x
+--R \|c
+--R +
+--R +-+
+--R +-+ +-+ x\|b
+--R (6a d - 2b c)\|b \|c atan(-----)
+--R +-+
+--R \|a
+--R /
+--R 3 2 2 2 2 +-+ +-+
+--R (4a d - 8a b c d + 4a b c )\|a \|c
+--R Type: Expression(Integer)
+--E 203
+
+--S 204 of 994
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 204
+
+)clear all
+
+--S 205 of 994
+t0:=1/((a+b*x^2)^2*(c+d*x^2)^2)
+--R
+--R
+--R (1)
+--R 1
+--R /
+--R 2 2 8 2 2 6 2 2 2 2 4
+--R b d x + (2a b d + 2b c d)x + (a d + 4a b c d + b c )x
+--R +
+--R 2 2 2 2 2
+--R (2a c d + 2a b c )x + a c
+--R Type: Fraction(Polynomial(Integer))
+--E 205
+
+--S 206 of 994
+r0:=1/2*d*(b*c+a*d)*x/(a*c*(b*c-a*d)^2*(c+d*x^2))+1/2*b*x/(a*(b*c-a*d)*_
+ (a+b*x^2)*(c+d*x^2))+1/2*b^(3/2)*(b*c-5*a*d)*atan(x*sqrt(b)/_
+ sqrt(a))/(a^(3/2)*(b*c-a*d)^3)+1/2*d^(3/2)*(5*b*c-a*d)*atan(x*_
+ sqrt(d)/sqrt(c))/(c^(3/2)*(b*c-a*d)^3)
+--R
+--R
+--R (2)
+--R 2 3 2 2 4 3 3 2 2 2 2 2 3 2
+--R (a b d - 5a b c d )x + (a d - 4a b c d - 5a b c d)x + a c d
+--R +
+--R 2 2
+--R - 5a b c d
+--R *
+--R +-+
+--R +-+ +-+ x\|d
+--R \|a \|d atan(-----)
+--R +-+
+--R \|c
+--R +
+--R 2 2 3 2 4 2 2 2 2 3 3 2 2 2
+--R (5a b c d - b c d)x + (5a b c d + 4a b c d - b c )x + 5a b c d
+--R +
+--R 2 3
+--R - a b c
+--R *
+--R +-+
+--R +-+ +-+ x\|b
+--R \|b \|c atan(-----)
+--R +-+
+--R \|a
+--R +
+--R 2 3 3 2 3 3 3 2 2 2 2 3 3 +-+ +-+
+--R ((a b d - b c d)x + (a d - a b c d + a b c d - b c )x)\|a \|c
+--R /
+--R 4 4 3 2 2 3 2 3 3 2 4 4 4
+--R (2a b c d - 6a b c d + 6a b c d - 2a b c d)x
+--R +
+--R 5 4 4 2 3 2 3 4 4 5 2 5 2 3 4 3 2
+--R (2a c d - 4a b c d + 4a b c d - 2a b c )x + 2a c d - 6a b c d
+--R +
+--R 3 2 4 2 3 5
+--R 6a b c d - 2a b c
+--R *
+--R +-+ +-+
+--R \|a \|c
+--R Type: Expression(Integer)
+--E 206
+
+--S 207 of 994
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R 2 2 3 2 4 2 2 2 2 3 3 2 2 2
+--R (5a b c d - b c d)x + (5a b c d + 4a b c d - b c )x + 5a b c d
+--R +
+--R 2 3
+--R - a b c
+--R *
+--R +---+
+--R | b 2
+--R +---+ 2a x |- - + b x - a
+--R | b \| a
+--R |- - log(---------------------)
+--R \| a 2
+--R b x + a
+--R +
+--R 2 3 2 2 4 3 3 2 2 2 2 2 3 2
+--R (a b d - 5a b c d )x + (a d - 4a b c d - 5a b c d)x + a c d
+--R +
+--R 2 2
+--R - 5a b c d
+--R *
+--R +---+
+--R | d 2
+--R +---+ 2c x |- - + d x - c
+--R | d \| c
+--R |- - log(---------------------)
+--R \| c 2
+--R d x + c
+--R +
+--R 2 3 3 2 3 3 3 2 2 2 2 3 3
+--R (2a b d - 2b c d)x + (2a d - 2a b c d + 2a b c d - 2b c )x
+--R /
+--R 4 4 3 2 2 3 2 3 3 2 4 4 4
+--R (4a b c d - 12a b c d + 12a b c d - 4a b c d)x
+--R +
+--R 5 4 4 2 3 2 3 4 4 5 2 5 2 3 4 3 2
+--R (4a c d - 8a b c d + 8a b c d - 4a b c )x + 4a c d - 12a b c d
+--R +
+--R 3 2 4 2 3 5
+--R 12a b c d - 4a b c
+--R ,
+--R
+--R 2 2 3 2 4 2 2 2 2 3 3 2 2 2
+--R (5a b c d - b c d)x + (5a b c d + 4a b c d - b c )x + 5a b c d
+--R +
+--R 2 3
+--R - a b c
+--R *
+--R +---+
+--R | b 2
+--R +---+ 2a x |- - + b x - a
+--R | b \| a
+--R |- - log(---------------------)
+--R \| a 2
+--R b x + a
+--R +
+--R 2 3 2 2 4 3 3 2 2 2 2 2
+--R (- 2a b d + 10a b c d )x + (- 2a d + 8a b c d + 10a b c d)x
+--R +
+--R 3 2 2 2
+--R - 2a c d + 10a b c d
+--R *
+--R +-+
+--R |d
+--R +-+ c |-
+--R |d \|c
+--R |- atan(-----)
+--R \|c d x
+--R +
+--R 2 3 3 2 3 3 3 2 2 2 2 3 3
+--R (2a b d - 2b c d)x + (2a d - 2a b c d + 2a b c d - 2b c )x
+--R /
+--R 4 4 3 2 2 3 2 3 3 2 4 4 4
+--R (4a b c d - 12a b c d + 12a b c d - 4a b c d)x
+--R +
+--R 5 4 4 2 3 2 3 4 4 5 2 5 2 3 4 3 2
+--R (4a c d - 8a b c d + 8a b c d - 4a b c )x + 4a c d - 12a b c d
+--R +
+--R 3 2 4 2 3 5
+--R 12a b c d - 4a b c
+--R ,
+--R
+--R 2 3 2 2 4 3 3 2 2 2 2 2 3 2
+--R (a b d - 5a b c d )x + (a d - 4a b c d - 5a b c d)x + a c d
+--R +
+--R 2 2
+--R - 5a b c d
+--R *
+--R +---+
+--R | d 2
+--R +---+ 2c x |- - + d x - c
+--R | d \| c
+--R |- - log(---------------------)
+--R \| c 2
+--R d x + c
+--R +
+--R 2 2 3 2 4 2 2 2 2 3 3 2
+--R (- 10a b c d + 2b c d)x + (- 10a b c d - 8a b c d + 2b c )x
+--R +
+--R 2 2 2 3
+--R - 10a b c d + 2a b c
+--R *
+--R +-+
+--R |b
+--R +-+ a |-
+--R |b \|a
+--R |- atan(-----)
+--R \|a b x
+--R +
+--R 2 3 3 2 3 3 3 2 2 2 2 3 3
+--R (2a b d - 2b c d)x + (2a d - 2a b c d + 2a b c d - 2b c )x
+--R /
+--R 4 4 3 2 2 3 2 3 3 2 4 4 4
+--R (4a b c d - 12a b c d + 12a b c d - 4a b c d)x
+--R +
+--R 5 4 4 2 3 2 3 4 4 5 2 5 2 3 4 3 2
+--R (4a c d - 8a b c d + 8a b c d - 4a b c )x + 4a c d - 12a b c d
+--R +
+--R 3 2 4 2 3 5
+--R 12a b c d - 4a b c
+--R ,
+--R
+--R 2 3 2 2 4 3 3 2 2 2 2 2
+--R (- a b d + 5a b c d )x + (- a d + 4a b c d + 5a b c d)x
+--R +
+--R 3 2 2 2
+--R - a c d + 5a b c d
+--R *
+--R +-+
+--R |d
+--R +-+ c |-
+--R |d \|c
+--R |- atan(-----)
+--R \|c d x
+--R +
+--R 2 2 3 2 4 2 2 2 2 3 3 2
+--R (- 5a b c d + b c d)x + (- 5a b c d - 4a b c d + b c )x
+--R +
+--R 2 2 2 3
+--R - 5a b c d + a b c
+--R *
+--R +-+
+--R |b
+--R +-+ a |-
+--R |b \|a
+--R |- atan(-----)
+--R \|a b x
+--R +
+--R 2 3 3 2 3 3 3 2 2 2 2 3 3
+--R (a b d - b c d)x + (a d - a b c d + a b c d - b c )x
+--R /
+--R 4 4 3 2 2 3 2 3 3 2 4 4 4
+--R (2a b c d - 6a b c d + 6a b c d - 2a b c d)x
+--R +
+--R 5 4 4 2 3 2 3 4 4 5 2 5 2 3 4 3 2
+--R (2a c d - 4a b c d + 4a b c d - 2a b c )x + 2a c d - 6a b c d
+--R +
+--R 3 2 4 2 3 5
+--R 6a b c d - 2a b c
+--R ]
+--R Type: Union(List(Expression(Integer)),...)
+--E 207
+
+--S 208 of 994
+m0a:=a0.1-r0
+--R
+--R
+--R (4)
+--R +---+
+--R | b 2
+--R +---+ 2a x |- - + b x - a
+--R 2 2 | b +-+ +-+ \| a
+--R (5a b c d - b c ) |- - \|a \|c log(---------------------)
+--R \| a 2
+--R b x + a
+--R +
+--R +---+
+--R | d 2
+--R +---+ 2c x |- - + d x - c
+--R 2 2 | d +-+ +-+ \| c
+--R (a d - 5a b c d) |- - \|a \|c log(---------------------)
+--R \| c 2
+--R d x + c
+--R +
+--R +-+
+--R 2 2 +-+ +-+ x\|d
+--R (- 2a d + 10a b c d)\|a \|d atan(-----)
+--R +-+
+--R \|c
+--R +
+--R +-+
+--R 2 2 +-+ +-+ x\|b
+--R (- 10a b c d + 2b c )\|b \|c atan(-----)
+--R +-+
+--R \|a
+--R /
+--R 4 3 3 2 2 2 2 3 3 4 +-+ +-+
+--R (4a c d - 12a b c d + 12a b c d - 4a b c )\|a \|c
+--R Type: Expression(Integer)
+--E 208
+
+--S 209 of 994
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 209
+
+--S 210 of 994
+m0b:=a0.2-r0
+--R
+--R
+--R (6)
+--R +---+
+--R | b 2
+--R +---+ 2a x |- - + b x - a
+--R 2 2 | b +-+ +-+ \| a
+--R (5a b c d - b c ) |- - \|a \|c log(---------------------)
+--R \| a 2
+--R b x + a
+--R +
+--R +-+
+--R 2 2 +-+ +-+ x\|d
+--R (- 2a d + 10a b c d)\|a \|d atan(-----)
+--R +-+
+--R \|c
+--R +
+--R +-+
+--R |d
+--R +-+ c |-
+--R 2 2 +-+ +-+ |d \|c
+--R (- 2a d + 10a b c d)\|a \|c |- atan(-----)
+--R \|c d x
+--R +
+--R +-+
+--R 2 2 +-+ +-+ x\|b
+--R (- 10a b c d + 2b c )\|b \|c atan(-----)
+--R +-+
+--R \|a
+--R /
+--R 4 3 3 2 2 2 2 3 3 4 +-+ +-+
+--R (4a c d - 12a b c d + 12a b c d - 4a b c )\|a \|c
+--R Type: Expression(Integer)
+--E 210
+
+--S 211 of 994
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 211
+
+)clear all
+
+--S 212 of 994
+t0:=1/((a+b*x^2)^2*(c+d*x^2)^3)
+--R
+--R
+--R (1)
+--R 1
+--R /
+--R 2 3 10 3 2 2 8 2 3 2 2 2 6
+--R b d x + (2a b d + 3b c d )x + (a d + 6a b c d + 3b c d)x
+--R +
+--R 2 2 2 2 3 4 2 2 3 2 2 3
+--R (3a c d + 6a b c d + b c )x + (3a c d + 2a b c )x + a c
+--R Type: Fraction(Polynomial(Integer))
+--E 212
+
+--S 213 of 994
+r0:=1/4*d*(2*b*c+a*d)*x/(a*c*(b*c-a*d)^2*(c+d*x^2)^2)+1/2*b*x/(a*(b*c-_
+ a*d)*(a+b*x^2)*(c+d*x^2)^2)+1/8*d*(4*b*c-a*d)*(b*c+3*a*d)*x/_
+ (a*c^2*(b*c-a*d)^3*(c+d*x^2))+1/2*b^(5/2)*(b*c-7*a*d)*atan(x*_
+ sqrt(b)/sqrt(a))/(a^(3/2)*(b*c-a*d)^4)+1/8*d^(3/2)*(35*b^2*c^2-_
+ 14*a*b*c*d+3*a^2*d^2)*atan(x*sqrt(d)/sqrt(c))/(c^(5/2)*(b*c-a*d)^4)
+--R
+--R
+--R (2)
+--R 3 5 2 2 4 3 2 3 6
+--R (3a b d - 14a b c d + 35a b c d )x
+--R +
+--R 4 5 3 4 2 2 2 3 3 3 2 4
+--R (3a d - 8a b c d + 7a b c d + 70a b c d )x
+--R +
+--R 4 4 3 2 3 2 2 3 2 3 4 2 4 2 3
+--R (6a c d - 25a b c d + 56a b c d + 35a b c d)x + 3a c d
+--R +
+--R 3 3 2 2 2 4
+--R - 14a b c d + 35a b c d
+--R *
+--R +-+
+--R +-+ +-+ x\|d
+--R \|a \|d atan(-----)
+--R +-+
+--R \|c
+--R +
+--R 3 2 3 4 3 2 6 2 2 2 3 3 3 2 4 4 4
+--R (- 28a b c d + 4b c d )x + (- 28a b c d - 52a b c d + 8b c d)x
+--R +
+--R 2 2 3 2 3 4 4 5 2 2 2 4 3 5
+--R (- 56a b c d - 20a b c d + 4b c )x - 28a b c d + 4a b c
+--R *
+--R +-+
+--R +-+ +-+ x\|b
+--R \|b \|c atan(-----)
+--R +-+
+--R \|a
+--R +
+--R 3 5 2 2 4 3 2 3 4 3 2 5
+--R (3a b d - 14a b c d + 7a b c d + 4b c d )x
+--R +
+--R 4 5 3 4 2 2 2 3 3 3 2 4 4 3
+--R (3a d - 9a b c d - 7a b c d + 5a b c d + 8b c d)x
+--R +
+--R 4 4 3 2 3 2 2 3 2 3 4 4 5
+--R (5a c d - 18a b c d + 13a b c d - 4a b c d + 4b c )x
+--R *
+--R +-+ +-+
+--R \|a \|c
+--R /
+--R 5 2 6 4 2 3 5 3 3 4 4 2 4 5 3 5 6 2 6
+--R (8a b c d - 32a b c d + 48a b c d - 32a b c d + 8a b c d )x
+--R +
+--R 6 2 6 5 3 5 4 2 4 4 3 3 5 3 2 4 6 2
+--R 8a c d - 16a b c d - 16a b c d + 64a b c d - 56a b c d
+--R +
+--R 5 7
+--R 16a b c d
+--R *
+--R 4
+--R x
+--R +
+--R 6 3 5 5 4 4 4 2 5 3 3 3 6 2 2 4 7
+--R 16a c d - 56a b c d + 64a b c d - 16a b c d - 16a b c d
+--R +
+--R 5 8
+--R 8a b c
+--R *
+--R 2
+--R x
+--R +
+--R 6 4 4 5 5 3 4 2 6 2 3 3 7 2 4 8
+--R 8a c d - 32a b c d + 48a b c d - 32a b c d + 8a b c
+--R *
+--R +-+ +-+
+--R \|a \|c
+--R Type: Expression(Integer)
+--E 213
+
+--S 214 of 994
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R 3 5 2 2 4 3 2 3 6
+--R (3a b d - 14a b c d + 35a b c d )x
+--R +
+--R 4 5 3 4 2 2 2 3 3 3 2 4
+--R (3a d - 8a b c d + 7a b c d + 70a b c d )x
+--R +
+--R 4 4 3 2 3 2 2 3 2 3 4 2 4 2 3
+--R (6a c d - 25a b c d + 56a b c d + 35a b c d)x + 3a c d
+--R +
+--R 3 3 2 2 2 4
+--R - 14a b c d + 35a b c d
+--R *
+--R +---+
+--R | d 2
+--R +---+ 2c x |- - + d x - c
+--R | d \| c
+--R |- - log(---------------------)
+--R \| c 2
+--R d x + c
+--R +
+--R 3 2 3 4 3 2 6 2 2 2 3 3 3 2 4 4 4
+--R (28a b c d - 4b c d )x + (28a b c d + 52a b c d - 8b c d)x
+--R +
+--R 2 2 3 2 3 4 4 5 2 2 2 4 3 5
+--R (56a b c d + 20a b c d - 4b c )x + 28a b c d - 4a b c
+--R *
+--R +---+
+--R | b 2
+--R +---+ - 2a x |- - + b x - a
+--R | b \| a
+--R |- - log(-----------------------)
+--R \| a 2
+--R b x + a
+--R +
+--R 3 5 2 2 4 3 2 3 4 3 2 5
+--R (6a b d - 28a b c d + 14a b c d + 8b c d )x
+--R +
+--R 4 5 3 4 2 2 2 3 3 3 2 4 4 3
+--R (6a d - 18a b c d - 14a b c d + 10a b c d + 16b c d)x
+--R +
+--R 4 4 3 2 3 2 2 3 2 3 4 4 5
+--R (10a c d - 36a b c d + 26a b c d - 8a b c d + 8b c )x
+--R /
+--R 5 2 6 4 2 3 5 3 3 4 4 2 4 5 3 5 6 2 6
+--R (16a b c d - 64a b c d + 96a b c d - 64a b c d + 16a b c d )x
+--R +
+--R 6 2 6 5 3 5 4 2 4 4 3 3 5 3 2 4 6 2
+--R 16a c d - 32a b c d - 32a b c d + 128a b c d - 112a b c d
+--R +
+--R 5 7
+--R 32a b c d
+--R *
+--R 4
+--R x
+--R +
+--R 6 3 5 5 4 4 4 2 5 3 3 3 6 2 2 4 7
+--R 32a c d - 112a b c d + 128a b c d - 32a b c d - 32a b c d
+--R +
+--R 5 8
+--R 16a b c
+--R *
+--R 2
+--R x
+--R +
+--R 6 4 4 5 5 3 4 2 6 2 3 3 7 2 4 8
+--R 16a c d - 64a b c d + 96a b c d - 64a b c d + 16a b c
+--R ,
+--R
+--R 3 2 3 4 3 2 6 2 2 2 3 3 3 2 4 4 4
+--R (14a b c d - 2b c d )x + (14a b c d + 26a b c d - 4b c d)x
+--R +
+--R 2 2 3 2 3 4 4 5 2 2 2 4 3 5
+--R (28a b c d + 10a b c d - 2b c )x + 14a b c d - 2a b c
+--R *
+--R +---+
+--R | b 2
+--R +---+ - 2a x |- - + b x - a
+--R | b \| a
+--R |- - log(-----------------------)
+--R \| a 2
+--R b x + a
+--R +
+--R 3 5 2 2 4 3 2 3 6
+--R (- 3a b d + 14a b c d - 35a b c d )x
+--R +
+--R 4 5 3 4 2 2 2 3 3 3 2 4
+--R (- 3a d + 8a b c d - 7a b c d - 70a b c d )x
+--R +
+--R 4 4 3 2 3 2 2 3 2 3 4 2 4 2 3
+--R (- 6a c d + 25a b c d - 56a b c d - 35a b c d)x - 3a c d
+--R +
+--R 3 3 2 2 2 4
+--R 14a b c d - 35a b c d
+--R *
+--R +-+
+--R |d
+--R +-+ c |-
+--R |d \|c
+--R |- atan(-----)
+--R \|c d x
+--R +
+--R 3 5 2 2 4 3 2 3 4 3 2 5
+--R (3a b d - 14a b c d + 7a b c d + 4b c d )x
+--R +
+--R 4 5 3 4 2 2 2 3 3 3 2 4 4 3
+--R (3a d - 9a b c d - 7a b c d + 5a b c d + 8b c d)x
+--R +
+--R 4 4 3 2 3 2 2 3 2 3 4 4 5
+--R (5a c d - 18a b c d + 13a b c d - 4a b c d + 4b c )x
+--R /
+--R 5 2 6 4 2 3 5 3 3 4 4 2 4 5 3 5 6 2 6
+--R (8a b c d - 32a b c d + 48a b c d - 32a b c d + 8a b c d )x
+--R +
+--R 6 2 6 5 3 5 4 2 4 4 3 3 5 3 2 4 6 2
+--R 8a c d - 16a b c d - 16a b c d + 64a b c d - 56a b c d
+--R +
+--R 5 7
+--R 16a b c d
+--R *
+--R 4
+--R x
+--R +
+--R 6 3 5 5 4 4 4 2 5 3 3 3 6 2 2 4 7
+--R 16a c d - 56a b c d + 64a b c d - 16a b c d - 16a b c d
+--R +
+--R 5 8
+--R 8a b c
+--R *
+--R 2
+--R x
+--R +
+--R 6 4 4 5 5 3 4 2 6 2 3 3 7 2 4 8
+--R 8a c d - 32a b c d + 48a b c d - 32a b c d + 8a b c
+--R ,
+--R
+--R 3 5 2 2 4 3 2 3 6
+--R (3a b d - 14a b c d + 35a b c d )x
+--R +
+--R 4 5 3 4 2 2 2 3 3 3 2 4
+--R (3a d - 8a b c d + 7a b c d + 70a b c d )x
+--R +
+--R 4 4 3 2 3 2 2 3 2 3 4 2 4 2 3
+--R (6a c d - 25a b c d + 56a b c d + 35a b c d)x + 3a c d
+--R +
+--R 3 3 2 2 2 4
+--R - 14a b c d + 35a b c d
+--R *
+--R +---+
+--R | d 2
+--R +---+ 2c x |- - + d x - c
+--R | d \| c
+--R |- - log(---------------------)
+--R \| c 2
+--R d x + c
+--R +
+--R 3 2 3 4 3 2 6 2 2 2 3 3 3 2 4 4 4
+--R (56a b c d - 8b c d )x + (56a b c d + 104a b c d - 16b c d)x
+--R +
+--R 2 2 3 2 3 4 4 5 2 2 2 4 3 5
+--R (112a b c d + 40a b c d - 8b c )x + 56a b c d - 8a b c
+--R *
+--R +-+
+--R |b
+--R +-+ a |-
+--R |b \|a
+--R |- atan(-----)
+--R \|a b x
+--R +
+--R 3 5 2 2 4 3 2 3 4 3 2 5
+--R (6a b d - 28a b c d + 14a b c d + 8b c d )x
+--R +
+--R 4 5 3 4 2 2 2 3 3 3 2 4 4 3
+--R (6a d - 18a b c d - 14a b c d + 10a b c d + 16b c d)x
+--R +
+--R 4 4 3 2 3 2 2 3 2 3 4 4 5
+--R (10a c d - 36a b c d + 26a b c d - 8a b c d + 8b c )x
+--R /
+--R 5 2 6 4 2 3 5 3 3 4 4 2 4 5 3 5 6 2 6
+--R (16a b c d - 64a b c d + 96a b c d - 64a b c d + 16a b c d )x
+--R +
+--R 6 2 6 5 3 5 4 2 4 4 3 3 5 3 2 4 6 2
+--R 16a c d - 32a b c d - 32a b c d + 128a b c d - 112a b c d
+--R +
+--R 5 7
+--R 32a b c d
+--R *
+--R 4
+--R x
+--R +
+--R 6 3 5 5 4 4 4 2 5 3 3 3 6 2 2 4 7
+--R 32a c d - 112a b c d + 128a b c d - 32a b c d - 32a b c d
+--R +
+--R 5 8
+--R 16a b c
+--R *
+--R 2
+--R x
+--R +
+--R 6 4 4 5 5 3 4 2 6 2 3 3 7 2 4 8
+--R 16a c d - 64a b c d + 96a b c d - 64a b c d + 16a b c
+--R ,
+--R
+--R 3 5 2 2 4 3 2 3 6
+--R (- 3a b d + 14a b c d - 35a b c d )x
+--R +
+--R 4 5 3 4 2 2 2 3 3 3 2 4
+--R (- 3a d + 8a b c d - 7a b c d - 70a b c d )x
+--R +
+--R 4 4 3 2 3 2 2 3 2 3 4 2 4 2 3
+--R (- 6a c d + 25a b c d - 56a b c d - 35a b c d)x - 3a c d
+--R +
+--R 3 3 2 2 2 4
+--R 14a b c d - 35a b c d
+--R *
+--R +-+
+--R |d
+--R +-+ c |-
+--R |d \|c
+--R |- atan(-----)
+--R \|c d x
+--R +
+--R 3 2 3 4 3 2 6 2 2 2 3 3 3 2 4 4 4
+--R (28a b c d - 4b c d )x + (28a b c d + 52a b c d - 8b c d)x
+--R +
+--R 2 2 3 2 3 4 4 5 2 2 2 4 3 5
+--R (56a b c d + 20a b c d - 4b c )x + 28a b c d - 4a b c
+--R *
+--R +-+
+--R |b
+--R +-+ a |-
+--R |b \|a
+--R |- atan(-----)
+--R \|a b x
+--R +
+--R 3 5 2 2 4 3 2 3 4 3 2 5
+--R (3a b d - 14a b c d + 7a b c d + 4b c d )x
+--R +
+--R 4 5 3 4 2 2 2 3 3 3 2 4 4 3
+--R (3a d - 9a b c d - 7a b c d + 5a b c d + 8b c d)x
+--R +
+--R 4 4 3 2 3 2 2 3 2 3 4 4 5
+--R (5a c d - 18a b c d + 13a b c d - 4a b c d + 4b c )x
+--R /
+--R 5 2 6 4 2 3 5 3 3 4 4 2 4 5 3 5 6 2 6
+--R (8a b c d - 32a b c d + 48a b c d - 32a b c d + 8a b c d )x
+--R +
+--R 6 2 6 5 3 5 4 2 4 4 3 3 5 3 2 4 6 2
+--R 8a c d - 16a b c d - 16a b c d + 64a b c d - 56a b c d
+--R +
+--R 5 7
+--R 16a b c d
+--R *
+--R 4
+--R x
+--R +
+--R 6 3 5 5 4 4 4 2 5 3 3 3 6 2 2 4 7
+--R 16a c d - 56a b c d + 64a b c d - 16a b c d - 16a b c d
+--R +
+--R 5 8
+--R 8a b c
+--R *
+--R 2
+--R x
+--R +
+--R 6 4 4 5 5 3 4 2 6 2 3 3 7 2 4 8
+--R 8a c d - 32a b c d + 48a b c d - 32a b c d + 8a b c
+--R ]
+--R Type: Union(List(Expression(Integer)),...)
+--E 214
+
+--S 215 of 994
+m0a:=a0.1-r0
+--R
+--R
+--R (4)
+--R +---+
+--R | d 2
+--R +---+ 2c x |- - + d x - c
+--R 3 3 2 2 2 2 | d +-+ +-+ \| c
+--R (3a d - 14a b c d + 35a b c d) |- - \|a \|c log(---------------------)
+--R \| c 2
+--R d x + c
+--R +
+--R +---+
+--R | b 2
+--R +---+ - 2a x |- - + b x - a
+--R 2 2 3 3 | b +-+ +-+ \| a
+--R (28a b c d - 4b c ) |- - \|a \|c log(-----------------------)
+--R \| a 2
+--R b x + a
+--R +
+--R +-+
+--R 3 3 2 2 2 2 +-+ +-+ x\|d
+--R (- 6a d + 28a b c d - 70a b c d)\|a \|d atan(-----)
+--R +-+
+--R \|c
+--R +
+--R +-+
+--R 2 2 3 3 +-+ +-+ x\|b
+--R (56a b c d - 8b c )\|b \|c atan(-----)
+--R +-+
+--R \|a
+--R /
+--R 5 2 4 4 3 3 3 2 4 2 2 3 5 4 6 +-+ +-+
+--R (16a c d - 64a b c d + 96a b c d - 64a b c d + 16a b c )\|a \|c
+--R Type: Expression(Integer)
+--E 215
+
+--S 216 of 994
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 216
+
+--S 217 of 994
+m0b:=a0.2-r0
+--R
+--R
+--R (6)
+--R +---+
+--R | b 2
+--R +---+ - 2a x |- - + b x - a
+--R 2 2 3 3 | b +-+ +-+ \| a
+--R (14a b c d - 2b c ) |- - \|a \|c log(-----------------------)
+--R \| a 2
+--R b x + a
+--R +
+--R +-+
+--R 3 3 2 2 2 2 +-+ +-+ x\|d
+--R (- 3a d + 14a b c d - 35a b c d)\|a \|d atan(-----)
+--R +-+
+--R \|c
+--R +
+--R +-+
+--R |d
+--R +-+ c |-
+--R 3 3 2 2 2 2 +-+ +-+ |d \|c
+--R (- 3a d + 14a b c d - 35a b c d)\|a \|c |- atan(-----)
+--R \|c d x
+--R +
+--R +-+
+--R 2 2 3 3 +-+ +-+ x\|b
+--R (28a b c d - 4b c )\|b \|c atan(-----)
+--R +-+
+--R \|a
+--R /
+--R 5 2 4 4 3 3 3 2 4 2 2 3 5 4 6 +-+ +-+
+--R (8a c d - 32a b c d + 48a b c d - 32a b c d + 8a b c )\|a \|c
+--R Type: Expression(Integer)
+--E 217
+
+--S 218 of 994
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 218
+
+)clear all
+
+--S 219 of 994
+t0:=(c+d*x^2)^5/(a+b*x^2)^3
+--R
+--R
+--R 5 10 4 8 2 3 6 3 2 4 4 2 5
+--R d x + 5c d x + 10c d x + 10c d x + 5c d x + c
+--R (1) ----------------------------------------------------
+--R 3 6 2 4 2 2 3
+--R b x + 3a b x + 3a b x + a
+--R Type: Fraction(Polynomial(Integer))
+--E 219
+
+--S 220 of 994
+r0:=d^3*(10*b^2*c^2-15*a*b*c*d+6*a^2*d^2)*x/b^5+1/3*d^4*(5*b*c-3*a*d)*_
+ x^3/b^4+1/5*d^5*x^5/b^3+1/4*(b*c-a*d)^5*x/(a*b^5*(a+b*x^2)^2)+_
+ 1/8*(b*c-a*d)^4*(3*b*c+17*a*d)*x/(a^2*b^5*(a+b*x^2))+1/8*(b*c-_
+ a*d)^3*(3*b^2*c^2+14*a*b*c*d+63*a^2*d^2)*atan(x*sqrt(b)/sqrt(a))/_
+ (a^(5/2)*b^(11/2))
+--R
+--R
+--R (2)
+--R 5 2 5 4 3 4 3 4 2 3 2 5 3 2
+--R - 945a b d + 2625a b c d - 2250a b c d + 450a b c d
+--R +
+--R 6 4 7 5
+--R 75a b c d + 45b c
+--R *
+--R 4
+--R x
+--R +
+--R 6 5 5 2 4 4 3 2 3 3 4 3 2
+--R - 1890a b d + 5250a b c d - 4500a b c d + 900a b c d
+--R +
+--R 2 5 4 6 5
+--R 150a b c d + 90a b c
+--R *
+--R 2
+--R x
+--R +
+--R 7 5 6 4 5 2 2 3 4 3 3 2 3 4 4
+--R - 945a d + 2625a b c d - 2250a b c d + 450a b c d + 75a b c d
+--R +
+--R 2 5 5
+--R 45a b c
+--R *
+--R +-+
+--R x\|b
+--R atan(-----)
+--R +-+
+--R \|a
+--R +
+--R 2 4 5 9 3 3 5 2 4 4 7
+--R 24a b d x + (- 72a b d + 200a b c d )x
+--R +
+--R 4 2 5 3 3 4 2 4 2 3 5
+--R (504a b d - 1400a b c d + 1200a b c d )x
+--R +
+--R 5 5 4 2 4 3 3 2 3 2 4 3 2
+--R 1575a b d - 4375a b c d + 3750a b c d - 750a b c d
+--R +
+--R 5 4 6 5
+--R 75a b c d + 45b c
+--R *
+--R 3
+--R x
+--R +
+--R 6 5 5 4 4 2 2 3 3 3 3 2 2 4 4
+--R 945a d - 2625a b c d + 2250a b c d - 450a b c d - 75a b c d
+--R +
+--R 5 5
+--R 75a b c
+--R *
+--R x
+--R *
+--R +-+ +-+
+--R \|a \|b
+--R /
+--R 2 7 4 3 6 2 4 5 +-+ +-+
+--R (120a b x + 240a b x + 120a b )\|a \|b
+--R Type: Expression(Integer)
+--E 220
+
+--S 221 of 994
+--a0:=integrate(t0,x)
+--E 221
+
+--S 222 of 994
+--m0:=a0-r0
+--E 222
+
+--S 223 of 994
+--d0:=D(m0,x)
+--E 223
+
+)clear all
+
+--S 224 of 994
+t0:=(c+d*x^2)^4/(a+b*x^2)^3
+--R
+--R
+--R 4 8 3 6 2 2 4 3 2 4
+--R d x + 4c d x + 6c d x + 4c d x + c
+--R (1) ---------------------------------------
+--R 3 6 2 4 2 2 3
+--R b x + 3a b x + 3a b x + a
+--R Type: Fraction(Polynomial(Integer))
+--E 224
+
+--S 225 of 994
+r0:=d^3*(4*b*c-3*a*d)*x/b^4+1/3*d^4*x^3/b^3+1/4*(b*c-a*d)^4*x/_
+ (a*b^4*(a+b*x^2)^2)+1/8*(b*c-a*d)^3*(3*b*c+13*a*d)*x/(a^2*b^4*_
+ (a+b*x^2))+1/8*(b*c-a*d)^2*(3*b^2*c^2+10*a*b*c*d+35*a^2*d^2)*_
+ atan(x*sqrt(b)/sqrt(a))/(a^(5/2)*b^(9/2))
+--R
+--R
+--R (2)
+--R 4 2 4 3 3 3 2 4 2 2 5 3 6 4 4
+--R (105a b d - 180a b c d + 54a b c d + 12a b c d + 9b c )x
+--R +
+--R 5 4 4 2 3 3 3 2 2 2 4 3 5 4 2
+--R (210a b d - 360a b c d + 108a b c d + 24a b c d + 18a b c )x
+--R +
+--R 6 4 5 3 4 2 2 2 3 3 3 2 4 4
+--R 105a d - 180a b c d + 54a b c d + 12a b c d + 9a b c
+--R *
+--R +-+
+--R x\|b
+--R atan(-----)
+--R +-+
+--R \|a
+--R +
+--R 2 3 4 7 3 2 4 2 3 3 5
+--R 8a b d x + (- 56a b d + 96a b c d )x
+--R +
+--R 4 4 3 2 3 2 3 2 2 4 3 5 4 3
+--R (- 175a b d + 300a b c d - 90a b c d + 12a b c d + 9b c )x
+--R +
+--R 5 4 4 3 3 2 2 2 2 3 3 4 4
+--R (- 105a d + 180a b c d - 54a b c d - 12a b c d + 15a b c )x
+--R *
+--R +-+ +-+
+--R \|a \|b
+--R /
+--R 2 6 4 3 5 2 4 4 +-+ +-+
+--R (24a b x + 48a b x + 24a b )\|a \|b
+--R Type: Expression(Integer)
+--E 225
+
+--S 226 of 994
+--a0:=integrate(t0,x)
+--E 226
+
+--S 227 of 994
+--m0:=a0-r0
+--E 227
+
+--S 228 of 994
+--d0:=D(m0,x)
+--E 228
+
+)clear all
+
+--S 229 of 994
+t0:=(c+d*x^2)^3/(a+b*x^2)^3
+--R
+--R
+--R 3 6 2 4 2 2 3
+--R d x + 3c d x + 3c d x + c
+--R (1) -----------------------------
+--R 3 6 2 4 2 2 3
+--R b x + 3a b x + 3a b x + a
+--R Type: Fraction(Polynomial(Integer))
+--E 229
+
+--S 230 of 994
+r0:=d^3*x/b^3+1/4*(b*c-a*d)^3*x/(a*b^3*(a+b*x^2)^2)+3/8*(b*c-a*d)^2*_
+ (b*c+3*a*d)*x/(a^2*b^3*(a+b*x^2))+3/8*(b*c-a*d)*(4*a^2*d^2+_
+ (b*c+a*d)^2)*atan(x*sqrt(b)/sqrt(a))/(a^(5/2)*b^(7/2))
+--R
+--R
+--R (2)
+--R 3 2 3 2 3 2 4 2 5 3 4
+--R (- 15a b d + 9a b c d + 3a b c d + 3b c )x
+--R +
+--R 4 3 3 2 2 2 3 2 4 3 2 5 3 4 2
+--R (- 30a b d + 18a b c d + 6a b c d + 6a b c )x - 15a d + 9a b c d
+--R +
+--R 3 2 2 2 3 3
+--R 3a b c d + 3a b c
+--R *
+--R +-+
+--R x\|b
+--R atan(-----)
+--R +-+
+--R \|a
+--R +
+--R 2 2 3 5 3 3 2 2 2 3 2 4 3 3
+--R 8a b d x + (25a b d - 15a b c d + 3a b c d + 3b c )x
+--R +
+--R 4 3 3 2 2 2 2 3 3
+--R (15a d - 9a b c d - 3a b c d + 5a b c )x
+--R *
+--R +-+ +-+
+--R \|a \|b
+--R /
+--R 2 5 4 3 4 2 4 3 +-+ +-+
+--R (8a b x + 16a b x + 8a b )\|a \|b
+--R Type: Expression(Integer)
+--E 230
+
+--S 231 of 994
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R 3 2 3 2 3 2 4 2 5 3 4
+--R (15a b d - 9a b c d - 3a b c d - 3b c )x
+--R +
+--R 4 3 3 2 2 2 3 2 4 3 2 5 3 4 2
+--R (30a b d - 18a b c d - 6a b c d - 6a b c )x + 15a d - 9a b c d
+--R +
+--R 3 2 2 2 3 3
+--R - 3a b c d - 3a b c
+--R *
+--R 2 +-----+
+--R (b x - a)\|- a b - 2a b x
+--R log(---------------------------)
+--R 2
+--R b x + a
+--R +
+--R 2 2 3 5 3 3 2 2 2 3 2 4 3 3
+--R 16a b d x + (50a b d - 30a b c d + 6a b c d + 6b c )x
+--R +
+--R 4 3 3 2 2 2 2 3 3
+--R (30a d - 18a b c d - 6a b c d + 10a b c )x
+--R *
+--R +-----+
+--R \|- a b
+--R /
+--R 2 5 4 3 4 2 4 3 +-----+
+--R (16a b x + 32a b x + 16a b )\|- a b
+--R ,
+--R
+--R 3 2 3 2 3 2 4 2 5 3 4
+--R (- 15a b d + 9a b c d + 3a b c d + 3b c )x
+--R +
+--R 4 3 3 2 2 2 3 2 4 3 2 5 3
+--R (- 30a b d + 18a b c d + 6a b c d + 6a b c )x - 15a d
+--R +
+--R 4 2 3 2 2 2 3 3
+--R 9a b c d + 3a b c d + 3a b c
+--R *
+--R +---+
+--R x\|a b
+--R atan(-------)
+--R a
+--R +
+--R 2 2 3 5 3 3 2 2 2 3 2 4 3 3
+--R 8a b d x + (25a b d - 15a b c d + 3a b c d + 3b c )x
+--R +
+--R 4 3 3 2 2 2 2 3 3
+--R (15a d - 9a b c d - 3a b c d + 5a b c )x
+--R *
+--R +---+
+--R \|a b
+--R /
+--R 2 5 4 3 4 2 4 3 +---+
+--R (8a b x + 16a b x + 8a b )\|a b
+--R ]
+--R Type: Union(List(Expression(Integer)),...)
+--E 231
+
+--S 232 of 994
+m0a:=a0.1-r0
+--R
+--R
+--R (4)
+--R 3 3 2 2 2 2 3 3 +-+ +-+
+--R (15a d - 9a b c d - 3a b c d - 3b c )\|a \|b
+--R *
+--R 2 +-----+
+--R (b x - a)\|- a b - 2a b x
+--R log(---------------------------)
+--R 2
+--R b x + a
+--R +
+--R +-+
+--R 3 3 2 2 2 2 3 3 +-----+ x\|b
+--R (30a d - 18a b c d - 6a b c d - 6b c )\|- a b atan(-----)
+--R +-+
+--R \|a
+--R /
+--R 2 3 +-----+ +-+ +-+
+--R 16a b \|- a b \|a \|b
+--R Type: Expression(Integer)
+--E 232
+
+--S 233 of 994
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 233
+
+--S 234 of 994
+m0b:=a0.2-r0
+--R
+--R
+--R (6)
+--R +---+
+--R 3 3 2 2 2 2 3 3 +-+ +-+ x\|a b
+--R (- 15a d + 9a b c d + 3a b c d + 3b c )\|a \|b atan(-------)
+--R a
+--R +
+--R +-+
+--R 3 3 2 2 2 2 3 3 +---+ x\|b
+--R (15a d - 9a b c d - 3a b c d - 3b c )\|a b atan(-----)
+--R +-+
+--R \|a
+--R /
+--R 2 3 +-+ +-+ +---+
+--R 8a b \|a \|b \|a b
+--R Type: Expression(Integer)
+--E 234
+
+--S 235 of 994
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 235
+
+)clear all
+
+--S 236 of 994
+t0:=(c+d*x^2)^2/(a+b*x^2)^3
+--R
+--R
+--R 2 4 2 2
+--R d x + 2c d x + c
+--R (1) -----------------------------
+--R 3 6 2 4 2 2 3
+--R b x + 3a b x + 3a b x + a
+--R Type: Fraction(Polynomial(Integer))
+--E 236
+
+--S 237 of 994
+r0:=3/8*(c^2/a^2-d^2/b^2)*x/(a+b*x^2)+1/4*(b*c-a*d)*x*(c+d*x^2)/_
+ (a*b*(a+b*x^2)^2)+1/8*(3*b^2*c^2+2*a*b*c*d+3*a^2*d^2)*_
+ atan(x*sqrt(b)/sqrt(a))/(a^(5/2)*b^(5/2))
+--R
+--R
+--R (2)
+--R 2 2 2 3 4 2 4 3 2 2 2 3 2 2
+--R (3a b d + 2a b c d + 3b c )x + (6a b d + 4a b c d + 6a b c )x
+--R +
+--R 4 2 3 2 2 2
+--R 3a d + 2a b c d + 3a b c
+--R *
+--R +-+
+--R x\|b
+--R atan(-----)
+--R +-+
+--R \|a
+--R +
+--R 2 2 2 3 2 3 3 2 2 2 2
+--R ((- 5a b d + 2a b c d + 3b c )x + (- 3a d - 2a b c d + 5a b c )x)
+--R *
+--R +-+ +-+
+--R \|a \|b
+--R /
+--R 2 4 4 3 3 2 4 2 +-+ +-+
+--R (8a b x + 16a b x + 8a b )\|a \|b
+--R Type: Expression(Integer)
+--E 237
+
+--S 238 of 994
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R 2 2 2 3 4 2 4 3 2 2 2 3 2 2
+--R (3a b d + 2a b c d + 3b c )x + (6a b d + 4a b c d + 6a b c )x
+--R +
+--R 4 2 3 2 2 2
+--R 3a d + 2a b c d + 3a b c
+--R *
+--R 2 +-----+
+--R (b x - a)\|- a b + 2a b x
+--R log(---------------------------)
+--R 2
+--R b x + a
+--R +
+--R 2 2 2 3 2 3
+--R (- 10a b d + 4a b c d + 6b c )x
+--R +
+--R 3 2 2 2 2
+--R (- 6a d - 4a b c d + 10a b c )x
+--R *
+--R +-----+
+--R \|- a b
+--R /
+--R 2 4 4 3 3 2 4 2 +-----+
+--R (16a b x + 32a b x + 16a b )\|- a b
+--R ,
+--R
+--R 2 2 2 3 4 2 4 3 2 2 2 3 2 2
+--R (3a b d + 2a b c d + 3b c )x + (6a b d + 4a b c d + 6a b c )x
+--R +
+--R 4 2 3 2 2 2
+--R 3a d + 2a b c d + 3a b c
+--R *
+--R +---+
+--R x\|a b
+--R atan(-------)
+--R a
+--R +
+--R 2 2 2 3 2 3 3 2 2 2 2
+--R ((- 5a b d + 2a b c d + 3b c )x + (- 3a d - 2a b c d + 5a b c )x)
+--R *
+--R +---+
+--R \|a b
+--R /
+--R 2 4 4 3 3 2 4 2 +---+
+--R (8a b x + 16a b x + 8a b )\|a b
+--R ]
+--R Type: Union(List(Expression(Integer)),...)
+--E 238
+
+--S 239 of 994
+m0a:=a0.1-r0
+--R
+--R
+--R (4)
+--R 2 +-----+
+--R 2 2 2 2 +-+ +-+ (b x - a)\|- a b + 2a b x
+--R (3a d + 2a b c d + 3b c )\|a \|b log(---------------------------)
+--R 2
+--R b x + a
+--R +
+--R +-+
+--R 2 2 2 2 +-----+ x\|b
+--R (- 6a d - 4a b c d - 6b c )\|- a b atan(-----)
+--R +-+
+--R \|a
+--R /
+--R 2 2 +-----+ +-+ +-+
+--R 16a b \|- a b \|a \|b
+--R Type: Expression(Integer)
+--E 239
+
+--S 240 of 994
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 240
+
+--S 241 of 994
+m0b:=a0.2-r0
+--R
+--R
+--R (6)
+--R +---+
+--R 2 2 2 2 +-+ +-+ x\|a b
+--R (3a d + 2a b c d + 3b c )\|a \|b atan(-------)
+--R a
+--R +
+--R +-+
+--R 2 2 2 2 +---+ x\|b
+--R (- 3a d - 2a b c d - 3b c )\|a b atan(-----)
+--R +-+
+--R \|a
+--R /
+--R 2 2 +-+ +-+ +---+
+--R 8a b \|a \|b \|a b
+--R Type: Expression(Integer)
+--E 241
+
+--S 242 of 994
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 242
+
+)clear all
+
+--S 243 of 994
+t0:=(c+d*x^2)/(a+b*x^2)^3
+--R
+--R
+--R 2
+--R d x + c
+--R (1) -----------------------------
+--R 3 6 2 4 2 2 3
+--R b x + 3a b x + 3a b x + a
+--R Type: Fraction(Polynomial(Integer))
+--E 243
+
+--S 244 of 994
+r0:=1/4*(b*c-a*d)*x/(a*b*(a+b*x^2)^2)+1/8*(3*b*c+a*d)*x/(a^2*b*(a+_
+ b*x^2))+1/8*(3*b*c+a*d)*atan(x*sqrt(b)/sqrt(a))/(a^(5/2)*b^(3/2))
+--R
+--R
+--R (2)
+--R +-+
+--R 2 3 4 2 2 2 3 2 x\|b
+--R ((a b d + 3b c)x + (2a b d + 6a b c)x + a d + 3a b c)atan(-----)
+--R +-+
+--R \|a
+--R +
+--R 2 3 2 +-+ +-+
+--R ((a b d + 3b c)x + (- a d + 5a b c)x)\|a \|b
+--R /
+--R 2 3 4 3 2 2 4 +-+ +-+
+--R (8a b x + 16a b x + 8a b)\|a \|b
+--R Type: Expression(Integer)
+--E 244
+
+--S 245 of 994
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R 2 3 4 2 2 2 3 2
+--R ((a b d + 3b c)x + (2a b d + 6a b c)x + a d + 3a b c)
+--R *
+--R 2 +-----+
+--R (b x - a)\|- a b + 2a b x
+--R log(---------------------------)
+--R 2
+--R b x + a
+--R +
+--R 2 3 2 +-----+
+--R ((2a b d + 6b c)x + (- 2a d + 10a b c)x)\|- a b
+--R /
+--R 2 3 4 3 2 2 4 +-----+
+--R (16a b x + 32a b x + 16a b)\|- a b
+--R ,
+--R
+--R +---+
+--R 2 3 4 2 2 2 3 2 x\|a b
+--R ((a b d + 3b c)x + (2a b d + 6a b c)x + a d + 3a b c)atan(-------)
+--R a
+--R +
+--R 2 3 2 +---+
+--R ((a b d + 3b c)x + (- a d + 5a b c)x)\|a b
+--R /
+--R 2 3 4 3 2 2 4 +---+
+--R (8a b x + 16a b x + 8a b)\|a b
+--R ]
+--R Type: Union(List(Expression(Integer)),...)
+--E 245
+
+--S 246 of 994
+m0a:=a0.1-r0
+--R
+--R
+--R (4)
+--R 2 +-----+
+--R +-+ +-+ (b x - a)\|- a b + 2a b x
+--R (a d + 3b c)\|a \|b log(---------------------------)
+--R 2
+--R b x + a
+--R +
+--R +-+
+--R +-----+ x\|b
+--R (- 2a d - 6b c)\|- a b atan(-----)
+--R +-+
+--R \|a
+--R /
+--R 2 +-----+ +-+ +-+
+--R 16a b\|- a b \|a \|b
+--R Type: Expression(Integer)
+--E 246
+
+--S 247 of 994
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 247
+
+--S 248 of 994
+m0b:=a0.2-r0
+--R
+--R
+--R +---+ +-+
+--R +-+ +-+ x\|a b +---+ x\|b
+--R (a d + 3b c)\|a \|b atan(-------) + (- a d - 3b c)\|a b atan(-----)
+--R a +-+
+--R \|a
+--R (6) -------------------------------------------------------------------
+--R 2 +-+ +-+ +---+
+--R 8a b\|a \|b \|a b
+--R Type: Expression(Integer)
+--E 248
+
+--S 249 of 994
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 249
+
+)clear all
+
+--S 250 of 994
+t0:=1/((a+b*x^2)^3*(c+d*x^2))
+--R
+--R
+--R (1)
+--R 1
+--R ------------------------------------------------------------------------
+--R 3 8 2 3 6 2 2 4 3 2 2 3
+--R b d x + (3a b d + b c)x + (3a b d + 3a b c)x + (a d + 3a b c)x + a c
+--R Type: Fraction(Polynomial(Integer))
+--E 250
+
+--S 251 of 994
+r0:=1/4*b*x/(a*(b*c-a*d)*(a+b*x^2)^2)+1/8*b*(3*b*c-7*a*d)*x/_
+ (a^2*(b*c-a*d)^2*(a+b*x^2))+1/8*(3*b^2*c^2-10*a*b*c*d+15*_
+ a^2*d^2)*atan(x*sqrt(b)/sqrt(a))*sqrt(b)/(a^(5/2)*(b*c-a*d)^3)-_
+ d^(5/2)*atan(x*sqrt(d)/sqrt(c))/((b*c-a*d)^3*sqrt(c))
+--R
+--R
+--R (2)
+--R +-+
+--R 2 2 2 4 3 2 2 4 2 +-+ +-+ x\|d
+--R (8a b d x + 16a b d x + 8a d )\|a \|d atan(-----)
+--R +-+
+--R \|c
+--R +
+--R 2 2 2 3 4 2 4
+--R (- 15a b d + 10a b c d - 3b c )x
+--R +
+--R 3 2 2 2 3 2 2 4 2 3 2 2 2
+--R (- 30a b d + 20a b c d - 6a b c )x - 15a d + 10a b c d - 3a b c
+--R *
+--R +-+
+--R +-+ +-+ x\|b
+--R \|b \|c atan(-----)
+--R +-+
+--R \|a
+--R +
+--R 2 2 2 3 4 2 3
+--R (- 7a b d + 10a b c d - 3b c )x
+--R +
+--R 3 2 2 2 3 2
+--R (- 9a b d + 14a b c d - 5a b c )x
+--R *
+--R +-+ +-+
+--R \|a \|c
+--R /
+--R 5 2 3 4 3 2 3 4 2 2 5 3 4
+--R (8a b d - 24a b c d + 24a b c d - 8a b c )x
+--R +
+--R 6 3 5 2 2 4 3 2 3 4 3 2 7 3 6 2
+--R (16a b d - 48a b c d + 48a b c d - 16a b c )x + 8a d - 24a b c d
+--R +
+--R 5 2 2 4 3 3
+--R 24a b c d - 8a b c
+--R *
+--R +-+ +-+
+--R \|a \|c
+--R Type: Expression(Integer)
+--E 251
+
+--S 252 of 994
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R +---+
+--R | d 2
+--R +---+ 2c x |- - + d x - c
+--R 2 2 2 4 3 2 2 4 2 | d \| c
+--R (8a b d x + 16a b d x + 8a d ) |- - log(---------------------)
+--R \| c 2
+--R d x + c
+--R +
+--R 2 2 2 3 4 2 4
+--R (15a b d - 10a b c d + 3b c )x
+--R +
+--R 3 2 2 2 3 2 2 4 2 3 2 2 2
+--R (30a b d - 20a b c d + 6a b c )x + 15a d - 10a b c d + 3a b c
+--R *
+--R +---+
+--R | b 2
+--R +---+ - 2a x |- - + b x - a
+--R | b \| a
+--R |- - log(-----------------------)
+--R \| a 2
+--R b x + a
+--R +
+--R 2 2 2 3 4 2 3 3 2 2 2 3 2
+--R (- 14a b d + 20a b c d - 6b c )x + (- 18a b d + 28a b c d - 10a b c )x
+--R /
+--R 5 2 3 4 3 2 3 4 2 2 5 3 4
+--R (16a b d - 48a b c d + 48a b c d - 16a b c )x
+--R +
+--R 6 3 5 2 2 4 3 2 3 4 3 2 7 3 6 2
+--R (32a b d - 96a b c d + 96a b c d - 32a b c )x + 16a d - 48a b c d
+--R +
+--R 5 2 2 4 3 3
+--R 48a b c d - 16a b c
+--R ,
+--R
+--R 2 2 2 3 4 2 4
+--R (15a b d - 10a b c d + 3b c )x
+--R +
+--R 3 2 2 2 3 2 2 4 2 3 2 2 2
+--R (30a b d - 20a b c d + 6a b c )x + 15a d - 10a b c d + 3a b c
+--R *
+--R +---+
+--R | b 2
+--R +---+ - 2a x |- - + b x - a
+--R | b \| a
+--R |- - log(-----------------------)
+--R \| a 2
+--R b x + a
+--R +
+--R +-+
+--R |d
+--R +-+ c |-
+--R 2 2 2 4 3 2 2 4 2 |d \|c
+--R (- 16a b d x - 32a b d x - 16a d ) |- atan(-----)
+--R \|c d x
+--R +
+--R 2 2 2 3 4 2 3 3 2 2 2 3 2
+--R (- 14a b d + 20a b c d - 6b c )x + (- 18a b d + 28a b c d - 10a b c )x
+--R /
+--R 5 2 3 4 3 2 3 4 2 2 5 3 4
+--R (16a b d - 48a b c d + 48a b c d - 16a b c )x
+--R +
+--R 6 3 5 2 2 4 3 2 3 4 3 2 7 3 6 2
+--R (32a b d - 96a b c d + 96a b c d - 32a b c )x + 16a d - 48a b c d
+--R +
+--R 5 2 2 4 3 3
+--R 48a b c d - 16a b c
+--R ,
+--R
+--R +---+
+--R | d 2
+--R +---+ 2c x |- - + d x - c
+--R 2 2 2 4 3 2 2 4 2 | d \| c
+--R (4a b d x + 8a b d x + 4a d ) |- - log(---------------------)
+--R \| c 2
+--R d x + c
+--R +
+--R 2 2 2 3 4 2 4
+--R (15a b d - 10a b c d + 3b c )x
+--R +
+--R 3 2 2 2 3 2 2 4 2 3 2 2 2
+--R (30a b d - 20a b c d + 6a b c )x + 15a d - 10a b c d + 3a b c
+--R *
+--R +-+
+--R |b
+--R +-+ a |-
+--R |b \|a
+--R |- atan(-----)
+--R \|a b x
+--R +
+--R 2 2 2 3 4 2 3 3 2 2 2 3 2
+--R (- 7a b d + 10a b c d - 3b c )x + (- 9a b d + 14a b c d - 5a b c )x
+--R /
+--R 5 2 3 4 3 2 3 4 2 2 5 3 4
+--R (8a b d - 24a b c d + 24a b c d - 8a b c )x
+--R +
+--R 6 3 5 2 2 4 3 2 3 4 3 2 7 3 6 2
+--R (16a b d - 48a b c d + 48a b c d - 16a b c )x + 8a d - 24a b c d
+--R +
+--R 5 2 2 4 3 3
+--R 24a b c d - 8a b c
+--R ,
+--R
+--R +-+
+--R |d
+--R +-+ c |-
+--R 2 2 2 4 3 2 2 4 2 |d \|c
+--R (- 8a b d x - 16a b d x - 8a d ) |- atan(-----)
+--R \|c d x
+--R +
+--R 2 2 2 3 4 2 4
+--R (15a b d - 10a b c d + 3b c )x
+--R +
+--R 3 2 2 2 3 2 2 4 2 3 2 2 2
+--R (30a b d - 20a b c d + 6a b c )x + 15a d - 10a b c d + 3a b c
+--R *
+--R +-+
+--R |b
+--R +-+ a |-
+--R |b \|a
+--R |- atan(-----)
+--R \|a b x
+--R +
+--R 2 2 2 3 4 2 3 3 2 2 2 3 2
+--R (- 7a b d + 10a b c d - 3b c )x + (- 9a b d + 14a b c d - 5a b c )x
+--R /
+--R 5 2 3 4 3 2 3 4 2 2 5 3 4
+--R (8a b d - 24a b c d + 24a b c d - 8a b c )x
+--R +
+--R 6 3 5 2 2 4 3 2 3 4 3 2 7 3 6 2
+--R (16a b d - 48a b c d + 48a b c d - 16a b c )x + 8a d - 24a b c d
+--R +
+--R 5 2 2 4 3 3
+--R 24a b c d - 8a b c
+--R ]
+--R Type: Union(List(Expression(Integer)),...)
+--E 252
+
+--S 253 of 994
+m0a:=a0.1-r0
+--R
+--R
+--R (4)
+--R +---+
+--R | d 2
+--R +---+ 2c x |- - + d x - c
+--R 2 2 | d +-+ +-+ \| c
+--R 8a d |- - \|a \|c log(---------------------)
+--R \| c 2
+--R d x + c
+--R +
+--R +---+
+--R | b 2
+--R +---+ - 2a x |- - + b x - a
+--R 2 2 2 2 | b +-+ +-+ \| a
+--R (15a d - 10a b c d + 3b c ) |- - \|a \|c log(-----------------------)
+--R \| a 2
+--R b x + a
+--R +
+--R +-+
+--R 2 2 +-+ +-+ x\|d
+--R - 16a d \|a \|d atan(-----)
+--R +-+
+--R \|c
+--R +
+--R +-+
+--R 2 2 2 2 +-+ +-+ x\|b
+--R (30a d - 20a b c d + 6b c )\|b \|c atan(-----)
+--R +-+
+--R \|a
+--R /
+--R 5 3 4 2 3 2 2 2 3 3 +-+ +-+
+--R (16a d - 48a b c d + 48a b c d - 16a b c )\|a \|c
+--R Type: Expression(Integer)
+--E 253
+
+--S 254 of 994
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 254
+
+--S 255 of 994
+m0b:=a0.2-r0
+--R
+--R
+--R (6)
+--R +---+
+--R | b 2
+--R +---+ - 2a x |- - + b x - a
+--R 2 2 2 2 | b +-+ +-+ \| a
+--R (15a d - 10a b c d + 3b c ) |- - \|a \|c log(-----------------------)
+--R \| a 2
+--R b x + a
+--R +
+--R +-+
+--R |d
+--R +-+ +-+ c |-
+--R 2 2 +-+ +-+ x\|d 2 2 +-+ +-+ |d \|c
+--R - 16a d \|a \|d atan(-----) - 16a d \|a \|c |- atan(-----)
+--R +-+ \|c d x
+--R \|c
+--R +
+--R +-+
+--R 2 2 2 2 +-+ +-+ x\|b
+--R (30a d - 20a b c d + 6b c )\|b \|c atan(-----)
+--R +-+
+--R \|a
+--R /
+--R 5 3 4 2 3 2 2 2 3 3 +-+ +-+
+--R (16a d - 48a b c d + 48a b c d - 16a b c )\|a \|c
+--R Type: Expression(Integer)
+--E 255
+
+--S 256 of 994
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 256
+
+)clear all
+
+--S 257 of 994
+t0:=1/((a+b*x^2)^3*(c+d*x^2)^2)
+--R
+--R
+--R (1)
+--R 1
+--R /
+--R 3 2 10 2 2 3 8 2 2 2 3 2 6
+--R b d x + (3a b d + 2b c d)x + (3a b d + 6a b c d + b c )x
+--R +
+--R 3 2 2 2 2 4 3 2 2 2 3 2
+--R (a d + 6a b c d + 3a b c )x + (2a c d + 3a b c )x + a c
+--R Type: Fraction(Polynomial(Integer))
+--E 257
+
+--S 258 of 994
+r0:=1/8*d*(b*c-4*a*d)*(3*b*c+a*d)*x/(a^2*c*(b*c-a*d)^3*(c+d*x^2))+_
+ 1/4*b*x/(a*(b*c-a*d)*(a+b*x^2)^2*(c+d*x^2))+3/8*b*(b*c-3*a*d)*_
+ x/(a^2*(b*c-a*d)^2*(a+b*x^2)*(c+d*x^2))+1/8*b^(3/2)*(3*b^2*c^2-_
+ 14*a*b*c*d+35*a^2*d^2)*atan(x*sqrt(b)/sqrt(a))/(a^(5/2)*(b*c-_
+ a*d)^4)-1/2*d^(5/2)*(7*b*c-a*d)*atan(x*sqrt(d)/sqrt(c))/_
+ (c^(3/2)*(b*c-a*d)^4)
+--R
+--R
+--R (2)
+--R 3 2 4 2 3 3 6 4 4 3 2 3 2 3 2 2 4
+--R (4a b d - 28a b c d )x + (8a b d - 52a b c d - 28a b c d )x
+--R +
+--R 5 4 4 3 3 2 2 2 2 5 3 4 2 2
+--R (4a d - 20a b c d - 56a b c d )x + 4a c d - 28a b c d
+--R *
+--R +-+
+--R +-+ +-+ x\|d
+--R \|a \|d atan(-----)
+--R +-+
+--R \|c
+--R +
+--R 2 3 3 4 2 2 5 3 6
+--R (35a b c d - 14a b c d + 3b c d)x
+--R +
+--R 3 2 3 2 3 2 2 4 3 5 4 4
+--R (70a b c d + 7a b c d - 8a b c d + 3b c )x
+--R +
+--R 4 3 3 2 2 2 2 3 3 4 4 2 4 2 2
+--R (35a b c d + 56a b c d - 25a b c d + 6a b c )x + 35a b c d
+--R +
+--R 3 2 3 2 3 4
+--R - 14a b c d + 3a b c
+--R *
+--R +-+
+--R +-+ +-+ x\|b
+--R \|b \|c atan(-----)
+--R +-+
+--R \|a
+--R +
+--R 3 2 4 2 3 3 4 2 2 5 3 5
+--R (4a b d + 7a b c d - 14a b c d + 3b c d)x
+--R +
+--R 4 4 3 2 3 2 3 2 2 4 3 5 4 3
+--R (8a b d + 5a b c d - 7a b c d - 9a b c d + 3b c )x
+--R +
+--R 5 4 4 3 3 2 2 2 2 3 3 4 4
+--R (4a d - 4a b c d + 13a b c d - 18a b c d + 5a b c )x
+--R *
+--R +-+ +-+
+--R \|a \|c
+--R /
+--R 6 2 5 5 3 2 4 4 4 3 3 3 5 4 2 2 6 5 6
+--R (8a b c d - 32a b c d + 48a b c d - 32a b c d + 8a b c d)x
+--R +
+--R 7 5 6 2 2 4 5 3 3 3 4 4 4 2 3 5 5
+--R 16a b c d - 56a b c d + 64a b c d - 16a b c d - 16a b c d
+--R +
+--R 2 6 6
+--R 8a b c
+--R *
+--R 4
+--R x
+--R +
+--R 8 5 7 2 4 6 2 3 3 5 3 4 2 4 4 5
+--R 8a c d - 16a b c d - 16a b c d + 64a b c d - 56a b c d
+--R +
+--R 3 5 6
+--R 16a b c
+--R *
+--R 2
+--R x
+--R +
+--R 8 2 4 7 3 3 6 2 4 2 5 3 5 4 4 6
+--R 8a c d - 32a b c d + 48a b c d - 32a b c d + 8a b c
+--R *
+--R +-+ +-+
+--R \|a \|c
+--R Type: Expression(Integer)
+--E 258
+
+--S 259 of 994
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R 2 3 3 4 2 2 5 3 6
+--R (35a b c d - 14a b c d + 3b c d)x
+--R +
+--R 3 2 3 2 3 2 2 4 3 5 4 4
+--R (70a b c d + 7a b c d - 8a b c d + 3b c )x
+--R +
+--R 4 3 3 2 2 2 2 3 3 4 4 2 4 2 2
+--R (35a b c d + 56a b c d - 25a b c d + 6a b c )x + 35a b c d
+--R +
+--R 3 2 3 2 3 4
+--R - 14a b c d + 3a b c
+--R *
+--R +---+
+--R | b 2
+--R +---+ 2a x |- - + b x - a
+--R | b \| a
+--R |- - log(---------------------)
+--R \| a 2
+--R b x + a
+--R +
+--R 3 2 4 2 3 3 6 4 4 3 2 3 2 3 2 2 4
+--R (4a b d - 28a b c d )x + (8a b d - 52a b c d - 28a b c d )x
+--R +
+--R 5 4 4 3 3 2 2 2 2 5 3 4 2 2
+--R (4a d - 20a b c d - 56a b c d )x + 4a c d - 28a b c d
+--R *
+--R +---+
+--R | d 2
+--R +---+ 2c x |- - + d x - c
+--R | d \| c
+--R |- - log(---------------------)
+--R \| c 2
+--R d x + c
+--R +
+--R 3 2 4 2 3 3 4 2 2 5 3 5
+--R (8a b d + 14a b c d - 28a b c d + 6b c d)x
+--R +
+--R 4 4 3 2 3 2 3 2 2 4 3 5 4 3
+--R (16a b d + 10a b c d - 14a b c d - 18a b c d + 6b c )x
+--R +
+--R 5 4 4 3 3 2 2 2 2 3 3 4 4
+--R (8a d - 8a b c d + 26a b c d - 36a b c d + 10a b c )x
+--R /
+--R 6 2 5 5 3 2 4 4 4 3 3 3 5 4 2 2 6 5 6
+--R (16a b c d - 64a b c d + 96a b c d - 64a b c d + 16a b c d)x
+--R +
+--R 7 5 6 2 2 4 5 3 3 3 4 4 4 2 3 5 5
+--R 32a b c d - 112a b c d + 128a b c d - 32a b c d - 32a b c d
+--R +
+--R 2 6 6
+--R 16a b c
+--R *
+--R 4
+--R x
+--R +
+--R 8 5 7 2 4 6 2 3 3 5 3 4 2 4 4 5
+--R 16a c d - 32a b c d - 32a b c d + 128a b c d - 112a b c d
+--R +
+--R 3 5 6
+--R 32a b c
+--R *
+--R 2
+--R x
+--R +
+--R 8 2 4 7 3 3 6 2 4 2 5 3 5 4 4 6
+--R 16a c d - 64a b c d + 96a b c d - 64a b c d + 16a b c
+--R ,
+--R
+--R 2 3 3 4 2 2 5 3 6
+--R (35a b c d - 14a b c d + 3b c d)x
+--R +
+--R 3 2 3 2 3 2 2 4 3 5 4 4
+--R (70a b c d + 7a b c d - 8a b c d + 3b c )x
+--R +
+--R 4 3 3 2 2 2 2 3 3 4 4 2 4 2 2
+--R (35a b c d + 56a b c d - 25a b c d + 6a b c )x + 35a b c d
+--R +
+--R 3 2 3 2 3 4
+--R - 14a b c d + 3a b c
+--R *
+--R +---+
+--R | b 2
+--R +---+ 2a x |- - + b x - a
+--R | b \| a
+--R |- - log(---------------------)
+--R \| a 2
+--R b x + a
+--R +
+--R 3 2 4 2 3 3 6
+--R (- 8a b d + 56a b c d )x
+--R +
+--R 4 4 3 2 3 2 3 2 2 4
+--R (- 16a b d + 104a b c d + 56a b c d )x
+--R +
+--R 5 4 4 3 3 2 2 2 2 5 3 4 2 2
+--R (- 8a d + 40a b c d + 112a b c d )x - 8a c d + 56a b c d
+--R *
+--R +-+
+--R |d
+--R +-+ c |-
+--R |d \|c
+--R |- atan(-----)
+--R \|c d x
+--R +
+--R 3 2 4 2 3 3 4 2 2 5 3 5
+--R (8a b d + 14a b c d - 28a b c d + 6b c d)x
+--R +
+--R 4 4 3 2 3 2 3 2 2 4 3 5 4 3
+--R (16a b d + 10a b c d - 14a b c d - 18a b c d + 6b c )x
+--R +
+--R 5 4 4 3 3 2 2 2 2 3 3 4 4
+--R (8a d - 8a b c d + 26a b c d - 36a b c d + 10a b c )x
+--R /
+--R 6 2 5 5 3 2 4 4 4 3 3 3 5 4 2 2 6 5 6
+--R (16a b c d - 64a b c d + 96a b c d - 64a b c d + 16a b c d)x
+--R +
+--R 7 5 6 2 2 4 5 3 3 3 4 4 4 2 3 5 5
+--R 32a b c d - 112a b c d + 128a b c d - 32a b c d - 32a b c d
+--R +
+--R 2 6 6
+--R 16a b c
+--R *
+--R 4
+--R x
+--R +
+--R 8 5 7 2 4 6 2 3 3 5 3 4 2 4 4 5
+--R 16a c d - 32a b c d - 32a b c d + 128a b c d - 112a b c d
+--R +
+--R 3 5 6
+--R 32a b c
+--R *
+--R 2
+--R x
+--R +
+--R 8 2 4 7 3 3 6 2 4 2 5 3 5 4 4 6
+--R 16a c d - 64a b c d + 96a b c d - 64a b c d + 16a b c
+--R ,
+--R
+--R 3 2 4 2 3 3 6 4 4 3 2 3 2 3 2 2 4
+--R (2a b d - 14a b c d )x + (4a b d - 26a b c d - 14a b c d )x
+--R +
+--R 5 4 4 3 3 2 2 2 2 5 3 4 2 2
+--R (2a d - 10a b c d - 28a b c d )x + 2a c d - 14a b c d
+--R *
+--R +---+
+--R | d 2
+--R +---+ 2c x |- - + d x - c
+--R | d \| c
+--R |- - log(---------------------)
+--R \| c 2
+--R d x + c
+--R +
+--R 2 3 3 4 2 2 5 3 6
+--R (- 35a b c d + 14a b c d - 3b c d)x
+--R +
+--R 3 2 3 2 3 2 2 4 3 5 4 4
+--R (- 70a b c d - 7a b c d + 8a b c d - 3b c )x
+--R +
+--R 4 3 3 2 2 2 2 3 3 4 4 2 4 2 2
+--R (- 35a b c d - 56a b c d + 25a b c d - 6a b c )x - 35a b c d
+--R +
+--R 3 2 3 2 3 4
+--R 14a b c d - 3a b c
+--R *
+--R +-+
+--R |b
+--R +-+ a |-
+--R |b \|a
+--R |- atan(-----)
+--R \|a b x
+--R +
+--R 3 2 4 2 3 3 4 2 2 5 3 5
+--R (4a b d + 7a b c d - 14a b c d + 3b c d)x
+--R +
+--R 4 4 3 2 3 2 3 2 2 4 3 5 4 3
+--R (8a b d + 5a b c d - 7a b c d - 9a b c d + 3b c )x
+--R +
+--R 5 4 4 3 3 2 2 2 2 3 3 4 4
+--R (4a d - 4a b c d + 13a b c d - 18a b c d + 5a b c )x
+--R /
+--R 6 2 5 5 3 2 4 4 4 3 3 3 5 4 2 2 6 5 6
+--R (8a b c d - 32a b c d + 48a b c d - 32a b c d + 8a b c d)x
+--R +
+--R 7 5 6 2 2 4 5 3 3 3 4 4 4 2 3 5 5
+--R 16a b c d - 56a b c d + 64a b c d - 16a b c d - 16a b c d
+--R +
+--R 2 6 6
+--R 8a b c
+--R *
+--R 4
+--R x
+--R +
+--R 8 5 7 2 4 6 2 3 3 5 3 4 2 4 4 5
+--R 8a c d - 16a b c d - 16a b c d + 64a b c d - 56a b c d
+--R +
+--R 3 5 6
+--R 16a b c
+--R *
+--R 2
+--R x
+--R +
+--R 8 2 4 7 3 3 6 2 4 2 5 3 5 4 4 6
+--R 8a c d - 32a b c d + 48a b c d - 32a b c d + 8a b c
+--R ,
+--R
+--R 3 2 4 2 3 3 6
+--R (- 4a b d + 28a b c d )x
+--R +
+--R 4 4 3 2 3 2 3 2 2 4
+--R (- 8a b d + 52a b c d + 28a b c d )x
+--R +
+--R 5 4 4 3 3 2 2 2 2 5 3 4 2 2
+--R (- 4a d + 20a b c d + 56a b c d )x - 4a c d + 28a b c d
+--R *
+--R +-+
+--R |d
+--R +-+ c |-
+--R |d \|c
+--R |- atan(-----)
+--R \|c d x
+--R +
+--R 2 3 3 4 2 2 5 3 6
+--R (- 35a b c d + 14a b c d - 3b c d)x
+--R +
+--R 3 2 3 2 3 2 2 4 3 5 4 4
+--R (- 70a b c d - 7a b c d + 8a b c d - 3b c )x
+--R +
+--R 4 3 3 2 2 2 2 3 3 4 4 2 4 2 2
+--R (- 35a b c d - 56a b c d + 25a b c d - 6a b c )x - 35a b c d
+--R +
+--R 3 2 3 2 3 4
+--R 14a b c d - 3a b c
+--R *
+--R +-+
+--R |b
+--R +-+ a |-
+--R |b \|a
+--R |- atan(-----)
+--R \|a b x
+--R +
+--R 3 2 4 2 3 3 4 2 2 5 3 5
+--R (4a b d + 7a b c d - 14a b c d + 3b c d)x
+--R +
+--R 4 4 3 2 3 2 3 2 2 4 3 5 4 3
+--R (8a b d + 5a b c d - 7a b c d - 9a b c d + 3b c )x
+--R +
+--R 5 4 4 3 3 2 2 2 2 3 3 4 4
+--R (4a d - 4a b c d + 13a b c d - 18a b c d + 5a b c )x
+--R /
+--R 6 2 5 5 3 2 4 4 4 3 3 3 5 4 2 2 6 5 6
+--R (8a b c d - 32a b c d + 48a b c d - 32a b c d + 8a b c d)x
+--R +
+--R 7 5 6 2 2 4 5 3 3 3 4 4 4 2 3 5 5
+--R 16a b c d - 56a b c d + 64a b c d - 16a b c d - 16a b c d
+--R +
+--R 2 6 6
+--R 8a b c
+--R *
+--R 4
+--R x
+--R +
+--R 8 5 7 2 4 6 2 3 3 5 3 4 2 4 4 5
+--R 8a c d - 16a b c d - 16a b c d + 64a b c d - 56a b c d
+--R +
+--R 3 5 6
+--R 16a b c
+--R *
+--R 2
+--R x
+--R +
+--R 8 2 4 7 3 3 6 2 4 2 5 3 5 4 4 6
+--R 8a c d - 32a b c d + 48a b c d - 32a b c d + 8a b c
+--R ]
+--R Type: Union(List(Expression(Integer)),...)
+--E 259
+
+--S 260 of 994
+m0a:=a0.1-r0
+--R
+--R
+--R (4)
+--R +---+
+--R | b 2
+--R +---+ 2a x |- - + b x - a
+--R 2 2 2 2 3 3 | b +-+ +-+ \| a
+--R (35a b c d - 14a b c d + 3b c ) |- - \|a \|c log(---------------------)
+--R \| a 2
+--R b x + a
+--R +
+--R +---+
+--R | d 2
+--R +---+ 2c x |- - + d x - c
+--R 3 3 2 2 | d +-+ +-+ \| c
+--R (4a d - 28a b c d ) |- - \|a \|c log(---------------------)
+--R \| c 2
+--R d x + c
+--R +
+--R +-+
+--R 3 3 2 2 +-+ +-+ x\|d
+--R (- 8a d + 56a b c d )\|a \|d atan(-----)
+--R +-+
+--R \|c
+--R +
+--R +-+
+--R 2 2 2 2 3 3 +-+ +-+ x\|b
+--R (- 70a b c d + 28a b c d - 6b c )\|b \|c atan(-----)
+--R +-+
+--R \|a
+--R /
+--R 6 4 5 2 3 4 2 3 2 3 3 4 2 4 5 +-+ +-+
+--R (16a c d - 64a b c d + 96a b c d - 64a b c d + 16a b c )\|a \|c
+--R Type: Expression(Integer)
+--E 260
+
+--S 261 of 994
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 261
+
+--S 262 of 994
+m0b:=a0.2-r0
+--R
+--R
+--R (6)
+--R +---+
+--R | b 2
+--R +---+ 2a x |- - + b x - a
+--R 2 2 2 2 3 3 | b +-+ +-+ \| a
+--R (35a b c d - 14a b c d + 3b c ) |- - \|a \|c log(---------------------)
+--R \| a 2
+--R b x + a
+--R +
+--R +-+
+--R 3 3 2 2 +-+ +-+ x\|d
+--R (- 8a d + 56a b c d )\|a \|d atan(-----)
+--R +-+
+--R \|c
+--R +
+--R +-+
+--R |d
+--R +-+ c |-
+--R 3 3 2 2 +-+ +-+ |d \|c
+--R (- 8a d + 56a b c d )\|a \|c |- atan(-----)
+--R \|c d x
+--R +
+--R +-+
+--R 2 2 2 2 3 3 +-+ +-+ x\|b
+--R (- 70a b c d + 28a b c d - 6b c )\|b \|c atan(-----)
+--R +-+
+--R \|a
+--R /
+--R 6 4 5 2 3 4 2 3 2 3 3 4 2 4 5 +-+ +-+
+--R (16a c d - 64a b c d + 96a b c d - 64a b c d + 16a b c )\|a \|c
+--R Type: Expression(Integer)
+--E 262
+
+--S 263 of 994
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 263
+
+)clear all
+
+--S 264 of 994
+t0:=1/((a+b*x^2)^3*(c+d*x^2)^3)
+--R
+--R
+--R (1)
+--R 1
+--R /
+--R 3 3 12 2 3 3 2 10 2 3 2 2 3 2 8
+--R b d x + (3a b d + 3b c d )x + (3a b d + 9a b c d + 3b c d)x
+--R +
+--R 3 3 2 2 2 2 3 3 6 3 2 2 2 2 3 4
+--R (a d + 9a b c d + 9a b c d + b c )x + (3a c d + 9a b c d + 3a b c )x
+--R +
+--R 3 2 2 3 2 3 3
+--R (3a c d + 3a b c )x + a c
+--R Type: Fraction(Polynomial(Integer))
+--E 264
+
+--S 265 of 994
+r0:=1/8*d*(3*b^2*c^2-13*a*b*c*d-2*a^2*d^2)*x/(a^2*c*(b*c-a*d)^3*_
+ (c+d*x^2)^2)+1/4*b*x/(a*(b*c-a*d)*(a+b*x^2)^2*(c+d*x^2)^2)+_
+ 1/8*b*(3*b*c-11*a*d)*x/(a^2*(b*c-a*d)^2*(a+b*x^2)*(c+d*x^2)^2)+_
+ 3/8*d*(b*c+a*d)*(b^2*c^2-6*a*b*c*d+a^2*d^2)*x/(a^2*c^2*(b*c-_
+ a*d)^4*(c+d*x^2))+3/8*b^(5/2)*(b^2*c^2-6*a*b*c*d+21*a^2*d^2)*_
+ atan(x*sqrt(b)/sqrt(a))/(a^(5/2)*(b*c-a*d)^5)-3/8*d^(5/2)*_
+ (21*b^2*c^2-6*a*b*c*d+a^2*d^2)*atan(x*sqrt(d)/sqrt(c))/_
+ (c^(5/2)*(b*c-a*d)^5)
+--R
+--R
+--R (2)
+--R 4 2 6 3 3 5 2 4 2 4 8
+--R (3a b d - 18a b c d + 63a b c d )x
+--R +
+--R 5 6 4 2 5 3 3 2 4 2 4 3 3 6
+--R (6a b d - 30a b c d + 90a b c d + 126a b c d )x
+--R +
+--R 6 6 5 5 4 2 2 4 3 3 3 3 2 4 4 2 4
+--R (3a d - 6a b c d - 6a b c d + 234a b c d + 63a b c d )x
+--R +
+--R 6 5 5 2 4 4 2 3 3 3 3 4 2 2 6 2 4
+--R (6a c d - 30a b c d + 90a b c d + 126a b c d )x + 3a c d
+--R +
+--R 5 3 3 4 2 4 2
+--R - 18a b c d + 63a b c d
+--R *
+--R +-+
+--R +-+ +-+ x\|d
+--R \|a \|d atan(-----)
+--R +-+
+--R \|c
+--R +
+--R 2 4 2 4 5 3 3 6 4 2 8
+--R (- 63a b c d + 18a b c d - 3b c d )x
+--R +
+--R 3 3 2 4 2 4 3 3 5 4 2 6 5 6
+--R (- 126a b c d - 90a b c d + 30a b c d - 6b c d)x
+--R +
+--R 4 2 2 4 3 3 3 3 2 4 4 2 5 5 6 6 4
+--R (- 63a b c d - 234a b c d + 6a b c d + 6a b c d - 3b c )x
+--R +
+--R 4 2 3 3 3 3 4 2 2 4 5 5 6 2 4 2 4 2
+--R (- 126a b c d - 90a b c d + 30a b c d - 6a b c )x - 63a b c d
+--R +
+--R 3 3 5 2 4 6
+--R 18a b c d - 3a b c
+--R *
+--R +-+
+--R +-+ +-+ x\|b
+--R \|b \|c atan(-----)
+--R +-+
+--R \|a
+--R +
+--R 4 2 6 3 3 5 5 3 3 6 4 2 7
+--R (3a b d - 18a b c d + 18a b c d - 3b c d )x
+--R +
+--R 5 6 4 2 5 3 3 2 4 2 4 3 3 5 4 2
+--R 6a b d - 31a b c d - 9a b c d + 9a b c d + 31a b c d
+--R +
+--R 6 5
+--R - 6b c d
+--R *
+--R 5
+--R x
+--R +
+--R 6 6 5 5 4 2 2 4 2 4 4 2 5 5 6 6 3
+--R (3a d - 8a b c d - 29a b c d + 29a b c d + 8a b c d - 3b c )x
+--R +
+--R 6 5 5 2 4 4 2 3 3 3 3 4 2 2 4 5 5 6
+--R (5a c d - 22a b c d + 17a b c d - 17a b c d + 22a b c d - 5a b c )x
+--R *
+--R +-+ +-+
+--R \|a \|c
+--R /
+--R 7 2 2 7 6 3 3 6 5 4 4 5 4 5 5 4 3 6 6 3
+--R 8a b c d - 40a b c d + 80a b c d - 80a b c d + 40a b c d
+--R +
+--R 2 7 7 2
+--R - 8a b c d
+--R *
+--R 8
+--R x
+--R +
+--R 8 2 7 7 2 3 6 6 3 4 5 4 5 6 3 3 6 7 2
+--R 16a b c d - 64a b c d + 80a b c d - 80a b c d + 64a b c d
+--R +
+--R 2 7 8
+--R - 16a b c d
+--R *
+--R 6
+--R x
+--R +
+--R 9 2 7 8 3 6 7 2 4 5 6 3 5 4 5 4 6 3
+--R 8a c d - 8a b c d - 72a b c d + 200a b c d - 200a b c d
+--R +
+--R 4 5 7 2 3 6 8 2 7 9
+--R 72a b c d + 8a b c d - 8a b c
+--R *
+--R 4
+--R x
+--R +
+--R 9 3 6 8 4 5 7 2 5 4 5 4 7 2 4 5 8
+--R 16a c d - 64a b c d + 80a b c d - 80a b c d + 64a b c d
+--R +
+--R 3 6 9
+--R - 16a b c
+--R *
+--R 2
+--R x
+--R +
+--R 9 4 5 8 5 4 7 2 6 3 6 3 7 2 5 4 8 4 5 9
+--R 8a c d - 40a b c d + 80a b c d - 80a b c d + 40a b c d - 8a b c
+--R *
+--R +-+ +-+
+--R \|a \|c
+--R Type: Expression(Integer)
+--E 265
+
+--S 266 of 994
+--a0:=integrate(t0,x)
+--E 266
+
+--S 267 of 994
+--m0:=a0-r0
+--E 267
+
+--S 268 of 994
+--d0:=D(m0,x)
+--E 268
+
+)clear all
+
+--S 269 of 994
+t0:=(-1+x^2)^3/(1+x^2)^4
+--R
+--R
+--R 6 4 2
+--R x - 3x + 3x - 1
+--R (1) ------------------------
+--R 8 6 4 2
+--R x + 4x + 6x + 4x + 1
+--R Type: Fraction(Polynomial(Integer))
+--E 269
+
+--S 270 of 994
+r0:=-1/3*x*(1-x^2)^2/(1+x^2)^3-2/3*x/(1+x^2)
+--R
+--R
+--R 5 2 3
+--R - x - - x - x
+--R 3
+--R (2) ------------------
+--R 6 4 2
+--R x + 3x + 3x + 1
+--R Type: Fraction(Polynomial(Fraction(Integer)))
+--E 270
+
+--S 271 of 994
+a0:=integrate(t0,x)
+--R
+--R
+--R 5 3
+--R - 3x - 2x - 3x
+--R (3) -------------------
+--R 6 4 2
+--R 3x + 9x + 9x + 3
+--R Type: Union(Expression(Integer),...)
+--E 271
+
+--S 272 of 994
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 272
+
+--S 273 of 994
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 273
+
+)clear all
+
+--S 274 of 994
+t0:=(-1+x^2)^4/(1+x^2)^5
+--R
+--R
+--R 8 6 4 2
+--R x - 4x + 6x - 4x + 1
+--R (1) ---------------------------------
+--R 10 8 6 4 2
+--R x + 5x + 10x + 10x + 5x + 1
+--R Type: Fraction(Polynomial(Integer))
+--E 274
+
+--S 275 of 994
+r0:=1/4*x*(1-x^2)^3/(1+x^2)^4+3/8*x*(1-x^2)/(1+x^2)^2+3/8*atan(x)
+--R
+--R
+--R 8 6 4 2 7 5 3
+--R (3x + 12x + 18x + 12x + 3)atan(x) - 5x + 3x - 3x + 5x
+--R (2) ------------------------------------------------------------
+--R 8 6 4 2
+--R 8x + 32x + 48x + 32x + 8
+--R Type: Expression(Integer)
+--E 275
+
+--S 276 of 994
+a0:=integrate(t0,x)
+--R
+--R
+--R 8 6 4 2 7 5 3
+--R (3x + 12x + 18x + 12x + 3)atan(x) - 5x + 3x - 3x + 5x
+--R (3) ------------------------------------------------------------
+--R 8 6 4 2
+--R 8x + 32x + 48x + 32x + 8
+--R Type: Union(Expression(Integer),...)
+--E 276
+
+--S 277 of 994
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 277
+
+--S 278 of 994
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 278
+
+)clear all
+
+--S 279 of 994
+t0:=(a+b*x^2)^(1/2)*(c+d*x^2)^3
+--R
+--R
+--R +--------+
+--R 3 6 2 4 2 2 3 | 2
+--R (1) (d x + 3c d x + 3c d x + c )\|b x + a
+--R Type: Expression(Integer)
+--E 279
+
+--S 280 of 994
+r0:=1/192*d*(88*b^2*c^2-68*a*b*c*d+15*a^2*d^2)*x*(a+b*x^2)^(3/2)/b^3+_
+ 1/8*d*x*(a+b*x^2)^(3/2)*(c+d*x^2)^2/b+1/48*d*x*(a+b*x^2)^(3/2)*_
+ (c*(8*b*c-a*d)+d*(12*b*c-5*a*d)*x^2)/b^2+1/128*a*(64*b^3*c^3-_
+ 48*a*b^2*c^2*d+24*a^2*b*c*d^2-5*a^3*d^3)*atanh(x*sqrt(b)/_
+ sqrt(a+b*x^2))/b^(7/2)+1/128*(64*b^3*c^3-48*a*b^2*c^2*d+24*_
+ a^2*b*c*d^2-5*a^3*d^3)*x*sqrt(a+b*x^2)/b^3
+--R
+--R
+--R (2)
+--R +-+
+--R 4 3 3 2 2 2 2 3 3 x\|b
+--R (- 15a d + 72a b c d - 144a b c d + 192a b c )atanh(-----------)
+--R +--------+
+--R | 2
+--R \|b x + a
+--R +
+--R 3 3 7 2 3 3 2 5
+--R 48b d x + (8a b d + 192b c d )x
+--R +
+--R 2 3 2 2 3 2 3
+--R (- 10a b d + 48a b c d + 288b c d)x
+--R +
+--R 3 3 2 2 2 2 3 3
+--R (15a d - 72a b c d + 144a b c d + 192b c )x
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|b \|b x + a
+--R /
+--R 3 +-+
+--R 384b \|b
+--R Type: Expression(Integer)
+--E 280
+
+--S 281 of 994
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R 4 3 3 3 4 2 2 5 2 6 3 6
+--R (120a b d - 576a b c d + 1152a b c d - 1536a b c )x
+--R +
+--R 5 2 3 4 3 2 3 4 2 2 5 3 4
+--R (1200a b d - 5760a b c d + 11520a b c d - 15360a b c )x
+--R +
+--R 6 3 5 2 2 4 3 2 3 4 3 2
+--R (2880a b d - 13824a b c d + 27648a b c d - 36864a b c )x
+--R +
+--R 7 3 6 2 5 2 2 4 3 3
+--R 1920a d - 9216a b c d + 18432a b c d - 24576a b c
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|a \|b x + a
+--R +
+--R 4 4 3 3 5 2 2 6 2 7 3 8
+--R (- 15a b d + 72a b c d - 144a b c d + 192a b c )x
+--R +
+--R 5 3 3 4 4 2 3 5 2 2 6 3 6
+--R (- 480a b d + 2304a b c d - 4608a b c d + 6144a b c )x
+--R +
+--R 6 2 3 5 3 2 4 4 2 3 5 3 4
+--R (- 2400a b d + 11520a b c d - 23040a b c d + 30720a b c )x
+--R +
+--R 7 3 6 2 2 5 3 2 4 4 3 2
+--R (- 3840a b d + 18432a b c d - 36864a b c d + 49152a b c )x
+--R +
+--R 8 3 7 2 6 2 2 5 3 3
+--R - 1920a d + 9216a b c d - 18432a b c d + 24576a b c
+--R *
+--R +--------+
+--R +-+ +-+ | 2 2 +-+ +-+
+--R (\|a \|b + b x)\|b x + a + (- b x - a)\|b - b x\|a
+--R log(--------------------------------------------------------)
+--R +--------+
+--R +-+ | 2
+--R \|a \|b x + a - a
+--R +
+--R 7 3 15 6 3 7 2 13
+--R - 48b d x + (- 1544a b d - 192b c d )x
+--R +
+--R 2 5 3 6 2 7 2 11
+--R (- 7926a b d - 6192a b c d - 288b c d)x
+--R +
+--R 3 4 3 2 5 2 6 2 7 3 9
+--R (- 13263a b d - 32184a b c d - 9360a b c d - 192b c )x
+--R +
+--R 4 3 3 3 4 2 2 5 2 6 3 7
+--R (- 7072a b d - 54528a b c d - 50688a b c d - 6144a b c )x
+--R +
+--R 5 2 3 4 3 2 3 4 2 2 5 3 5
+--R (- 864a b d - 25344a b c d - 96768a b c d - 30720a b c )x
+--R +
+--R 6 3 5 2 2 4 3 2 3 4 3 3
+--R (- 2560a b d + 12288a b c d - 73728a b c d - 49152a b c )x
+--R +
+--R 7 3 6 2 5 2 2 4 3 3
+--R (- 1920a d + 9216a b c d - 18432a b c d - 24576a b c )x
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|b \|b x + a
+--R +
+--R 7 3 15 6 3 7 2 13
+--R 384b d x + (4288a b d + 1536b c d )x
+--R +
+--R 2 5 3 6 2 7 2 11
+--R (13680a b d + 17280a b c d + 2304b c d)x
+--R +
+--R 3 4 3 2 5 2 6 2 7 3 9
+--R (16776a b d + 55872a b c d + 26496a b c d + 1536b c )x
+--R +
+--R 4 3 3 3 4 2 2 5 2 6 3 7
+--R (7304a b d + 68160a b c d + 91008a b c d + 16896a b c )x
+--R +
+--R 5 2 3 4 3 2 3 4 2 2 5 3 5
+--R (1904a b d + 20352a b c d + 131328a b c d + 52224a b c )x
+--R +
+--R 6 3 5 2 2 4 3 2 3 4 3 3
+--R (3520a b d - 16896a b c d + 82944a b c d + 61440a b c )x
+--R +
+--R 7 3 6 2 5 2 2 4 3 3
+--R (1920a d - 9216a b c d + 18432a b c d + 24576a b c )x
+--R *
+--R +-+ +-+
+--R \|a \|b
+--R /
+--R +--------+
+--R 6 6 5 4 2 4 2 3 3 +-+ +-+ | 2
+--R (3072b x + 30720a b x + 73728a b x + 49152a b )\|a \|b \|b x + a
+--R +
+--R 7 8 6 6 2 5 4 3 4 2 4 3 +-+
+--R (- 384b x - 12288a b x - 61440a b x - 98304a b x - 49152a b )\|b
+--R ,
+--R
+--R 4 3 3 3 4 2 2 5 2 6 3 6
+--R (- 240a b d + 1152a b c d - 2304a b c d + 3072a b c )x
+--R +
+--R 5 2 3 4 3 2 3 4 2 2 5 3 4
+--R (- 2400a b d + 11520a b c d - 23040a b c d + 30720a b c )x
+--R +
+--R 6 3 5 2 2 4 3 2 3 4 3 2
+--R (- 5760a b d + 27648a b c d - 55296a b c d + 73728a b c )x
+--R +
+--R 7 3 6 2 5 2 2 4 3 3
+--R - 3840a d + 18432a b c d - 36864a b c d + 49152a b c
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|a \|b x + a
+--R +
+--R 4 4 3 3 5 2 2 6 2 7 3 8
+--R (30a b d - 144a b c d + 288a b c d - 384a b c )x
+--R +
+--R 5 3 3 4 4 2 3 5 2 2 6 3 6
+--R (960a b d - 4608a b c d + 9216a b c d - 12288a b c )x
+--R +
+--R 6 2 3 5 3 2 4 4 2 3 5 3 4
+--R (4800a b d - 23040a b c d + 46080a b c d - 61440a b c )x
+--R +
+--R 7 3 6 2 2 5 3 2 4 4 3 2
+--R (7680a b d - 36864a b c d + 73728a b c d - 98304a b c )x
+--R +
+--R 8 3 7 2 6 2 2 5 3 3
+--R 3840a d - 18432a b c d + 36864a b c d - 49152a b c
+--R *
+--R +--------+
+--R +---+ | 2 +---+ +-+
+--R \|- b \|b x + a - \|- b \|a
+--R atan(------------------------------)
+--R b x
+--R +
+--R 7 3 15 6 3 7 2 13
+--R - 48b d x + (- 1544a b d - 192b c d )x
+--R +
+--R 2 5 3 6 2 7 2 11
+--R (- 7926a b d - 6192a b c d - 288b c d)x
+--R +
+--R 3 4 3 2 5 2 6 2 7 3 9
+--R (- 13263a b d - 32184a b c d - 9360a b c d - 192b c )x
+--R +
+--R 4 3 3 3 4 2 2 5 2 6 3 7
+--R (- 7072a b d - 54528a b c d - 50688a b c d - 6144a b c )x
+--R +
+--R 5 2 3 4 3 2 3 4 2 2 5 3 5
+--R (- 864a b d - 25344a b c d - 96768a b c d - 30720a b c )x
+--R +
+--R 6 3 5 2 2 4 3 2 3 4 3 3
+--R (- 2560a b d + 12288a b c d - 73728a b c d - 49152a b c )x
+--R +
+--R 7 3 6 2 5 2 2 4 3 3
+--R (- 1920a d + 9216a b c d - 18432a b c d - 24576a b c )x
+--R *
+--R +--------+
+--R +---+ | 2
+--R \|- b \|b x + a
+--R +
+--R 7 3 15 6 3 7 2 13
+--R 384b d x + (4288a b d + 1536b c d )x
+--R +
+--R 2 5 3 6 2 7 2 11
+--R (13680a b d + 17280a b c d + 2304b c d)x
+--R +
+--R 3 4 3 2 5 2 6 2 7 3 9
+--R (16776a b d + 55872a b c d + 26496a b c d + 1536b c )x
+--R +
+--R 4 3 3 3 4 2 2 5 2 6 3 7
+--R (7304a b d + 68160a b c d + 91008a b c d + 16896a b c )x
+--R +
+--R 5 2 3 4 3 2 3 4 2 2 5 3 5
+--R (1904a b d + 20352a b c d + 131328a b c d + 52224a b c )x
+--R +
+--R 6 3 5 2 2 4 3 2 3 4 3 3
+--R (3520a b d - 16896a b c d + 82944a b c d + 61440a b c )x
+--R +
+--R 7 3 6 2 5 2 2 4 3 3
+--R (1920a d - 9216a b c d + 18432a b c d + 24576a b c )x
+--R *
+--R +---+ +-+
+--R \|- b \|a
+--R /
+--R +--------+
+--R 6 6 5 4 2 4 2 3 3 +---+ +-+ | 2
+--R (3072b x + 30720a b x + 73728a b x + 49152a b )\|- b \|a \|b x + a
+--R +
+--R 7 8 6 6 2 5 4 3 4 2 4 3 +---+
+--R (- 384b x - 12288a b x - 61440a b x - 98304a b x - 49152a b )\|- b
+--R ]
+--R Type: Union(List(Expression(Integer)),...)
+--E 281
+
+--S 282 of 994
+m0a:=a0.1-r0
+--R
+--R
+--R (4)
+--R 4 3 3 2 2 2 2 3 3
+--R (5a d - 24a b c d + 48a b c d - 64a b c )
+--R *
+--R +--------+
+--R +-+ +-+ | 2 2 +-+ +-+
+--R (\|a \|b + b x)\|b x + a + (- b x - a)\|b - b x\|a
+--R log(--------------------------------------------------------)
+--R +--------+
+--R +-+ | 2
+--R \|a \|b x + a - a
+--R +
+--R +-+
+--R 4 3 3 2 2 2 2 3 3 x\|b
+--R (5a d - 24a b c d + 48a b c d - 64a b c )atanh(-----------)
+--R +--------+
+--R | 2
+--R \|b x + a
+--R /
+--R 3 +-+
+--R 128b \|b
+--R Type: Expression(Integer)
+--E 282
+
+--S 283 of 994
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 283
+
+--S 284 of 994
+m0b:=a0.2-r0
+--R
+--R
+--R (6)
+--R +-+
+--R 4 3 3 2 2 2 2 3 3 +---+ x\|b
+--R (5a d - 24a b c d + 48a b c d - 64a b c )\|- b atanh(-----------)
+--R +--------+
+--R | 2
+--R \|b x + a
+--R +
+--R 4 3 3 2 2 2 2 3 3 +-+
+--R (- 10a d + 48a b c d - 96a b c d + 128a b c )\|b
+--R *
+--R +--------+
+--R +---+ | 2 +---+ +-+
+--R \|- b \|b x + a - \|- b \|a
+--R atan(------------------------------)
+--R b x
+--R /
+--R 3 +---+ +-+
+--R 128b \|- b \|b
+--R Type: Expression(Integer)
+--E 284
+
+--S 285 of 994
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 285
+
+)clear all
+
+--S 286 of 994
+t0:=(a+b*x^2)^(1/2)*(c+d*x^2)^2
+--R
+--R
+--R +--------+
+--R 2 4 2 2 | 2
+--R (1) (d x + 2c d x + c )\|b x + a
+--R Type: Expression(Integer)
+--E 286
+
+--S 287 of 994
+r0:=1/24*d*(8*b*c-3*a*d)*x*(a+b*x^2)^(3/2)/b^2+1/6*d*x*(a+b*x^2)^(3/2)*_
+ (c+d*x^2)/b+1/16*a*(8*b^2*c^2-4*a*b*c*d+a^2*d^2)*atanh(x*_
+ sqrt(b)/sqrt(a+b*x^2))/b^(5/2)+1/16*(8*b^2*c^2-4*a*b*c*d+_
+ a^2*d^2)*x*sqrt(a+b*x^2)/b^2
+--R
+--R
+--R (2)
+--R +-+
+--R 3 2 2 2 2 x\|b
+--R (3a d - 12a b c d + 24a b c )atanh(-----------)
+--R +--------+
+--R | 2
+--R \|b x + a
+--R +
+--R 2 2 5 2 2 3 2 2 2 2 +-+
+--R (8b d x + (2a b d + 24b c d)x + (- 3a d + 12a b c d + 24b c )x)\|b
+--R *
+--R +--------+
+--R | 2
+--R \|b x + a
+--R /
+--R 2 +-+
+--R 48b \|b
+--R Type: Expression(Integer)
+--E 287
+
+--S 288 of 994
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R 3 2 2 2 3 4 2 4
+--R (18a b d - 72a b c d + 144a b c )x
+--R +
+--R 4 2 3 2 2 3 2 2 5 2 4
+--R (96a b d - 384a b c d + 768a b c )x + 96a d - 384a b c d
+--R +
+--R 3 2 2
+--R 768a b c
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|a \|b x + a
+--R +
+--R 3 3 2 2 4 5 2 6
+--R (- 3a b d + 12a b c d - 24a b c )x
+--R +
+--R 4 2 2 3 3 2 4 2 4
+--R (- 54a b d + 216a b c d - 432a b c )x
+--R +
+--R 5 2 4 2 3 3 2 2 6 2 5
+--R (- 144a b d + 576a b c d - 1152a b c )x - 96a d + 384a b c d
+--R +
+--R 4 2 2
+--R - 768a b c
+--R *
+--R +--------+
+--R +-+ +-+ | 2 2 +-+ +-+
+--R (\|a \|b - b x)\|b x + a + (- b x - a)\|b + b x\|a
+--R log(--------------------------------------------------------)
+--R +--------+
+--R +-+ | 2
+--R \|a \|b x + a - a
+--R +
+--R 5 2 11 4 2 5 9
+--R - 8b d x + (- 146a b d - 24b c d)x
+--R +
+--R 2 3 2 4 5 2 7
+--R (- 417a b d - 444a b c d - 24b c )x
+--R +
+--R 3 2 2 2 3 4 2 5
+--R (- 298a b d - 1368a b c d - 432a b c )x
+--R +
+--R 4 2 3 2 2 3 2 3
+--R (80a b d - 1344a b c d - 1152a b c )x
+--R +
+--R 5 2 4 3 2 2
+--R (96a d - 384a b c d - 768a b c )x
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|b \|b x + a
+--R +
+--R 5 2 11 4 2 5 9
+--R 48b d x + (316a b d + 144b c d)x
+--R +
+--R 2 3 2 4 5 2 7
+--R (570a b d + 984a b c d + 144b c )x
+--R +
+--R 3 2 2 2 3 4 2 5
+--R (270a b d + 1992a b c d + 912a b c )x
+--R +
+--R 4 2 3 2 2 3 2 3
+--R (- 128a b d + 1536a b c d + 1536a b c )x
+--R +
+--R 5 2 4 3 2 2
+--R (- 96a d + 384a b c d + 768a b c )x
+--R *
+--R +-+ +-+
+--R \|a \|b
+--R /
+--R +--------+
+--R 4 4 3 2 2 2 +-+ +-+ | 2
+--R (288b x + 1536a b x + 1536a b )\|a \|b \|b x + a
+--R +
+--R 5 6 4 4 2 3 2 3 2 +-+
+--R (- 48b x - 864a b x - 2304a b x - 1536a b )\|b
+--R ,
+--R
+--R 3 2 2 2 3 4 2 4
+--R (36a b d - 144a b c d + 288a b c )x
+--R +
+--R 4 2 3 2 2 3 2 2 5 2 4
+--R (192a b d - 768a b c d + 1536a b c )x + 192a d - 768a b c d
+--R +
+--R 3 2 2
+--R 1536a b c
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|a \|b x + a
+--R +
+--R 3 3 2 2 4 5 2 6
+--R (- 6a b d + 24a b c d - 48a b c )x
+--R +
+--R 4 2 2 3 3 2 4 2 4
+--R (- 108a b d + 432a b c d - 864a b c )x
+--R +
+--R 5 2 4 2 3 3 2 2 6 2 5
+--R (- 288a b d + 1152a b c d - 2304a b c )x - 192a d + 768a b c d
+--R +
+--R 4 2 2
+--R - 1536a b c
+--R *
+--R +--------+
+--R +---+ | 2 +---+ +-+
+--R \|- b \|b x + a - \|- b \|a
+--R atan(------------------------------)
+--R b x
+--R +
+--R 5 2 11 4 2 5 9
+--R - 8b d x + (- 146a b d - 24b c d)x
+--R +
+--R 2 3 2 4 5 2 7
+--R (- 417a b d - 444a b c d - 24b c )x
+--R +
+--R 3 2 2 2 3 4 2 5
+--R (- 298a b d - 1368a b c d - 432a b c )x
+--R +
+--R 4 2 3 2 2 3 2 3
+--R (80a b d - 1344a b c d - 1152a b c )x
+--R +
+--R 5 2 4 3 2 2
+--R (96a d - 384a b c d - 768a b c )x
+--R *
+--R +--------+
+--R +---+ | 2
+--R \|- b \|b x + a
+--R +
+--R 5 2 11 4 2 5 9
+--R 48b d x + (316a b d + 144b c d)x
+--R +
+--R 2 3 2 4 5 2 7
+--R (570a b d + 984a b c d + 144b c )x
+--R +
+--R 3 2 2 2 3 4 2 5
+--R (270a b d + 1992a b c d + 912a b c )x
+--R +
+--R 4 2 3 2 2 3 2 3
+--R (- 128a b d + 1536a b c d + 1536a b c )x
+--R +
+--R 5 2 4 3 2 2
+--R (- 96a d + 384a b c d + 768a b c )x
+--R *
+--R +---+ +-+
+--R \|- b \|a
+--R /
+--R +--------+
+--R 4 4 3 2 2 2 +---+ +-+ | 2
+--R (288b x + 1536a b x + 1536a b )\|- b \|a \|b x + a
+--R +
+--R 5 6 4 4 2 3 2 3 2 +---+
+--R (- 48b x - 864a b x - 2304a b x - 1536a b )\|- b
+--R ]
+--R Type: Union(List(Expression(Integer)),...)
+--E 288
+
+--S 289 of 994
+m0a:=a0.1-r0
+--R
+--R
+--R (4)
+--R 3 2 2 2 2
+--R (a d - 4a b c d + 8a b c )
+--R *
+--R +--------+
+--R +-+ +-+ | 2 2 +-+ +-+
+--R (\|a \|b - b x)\|b x + a + (- b x - a)\|b + b x\|a
+--R log(--------------------------------------------------------)
+--R +--------+
+--R +-+ | 2
+--R \|a \|b x + a - a
+--R +
+--R +-+
+--R 3 2 2 2 2 x\|b
+--R (- a d + 4a b c d - 8a b c )atanh(-----------)
+--R +--------+
+--R | 2
+--R \|b x + a
+--R /
+--R 2 +-+
+--R 16b \|b
+--R Type: Expression(Integer)
+--E 289
+
+--S 290 of 994
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 290
+
+--S 291 of 994
+m0b:=a0.2-r0
+--R
+--R
+--R (6)
+--R +-+
+--R 3 2 2 2 2 +---+ x\|b
+--R (- a d + 4a b c d - 8a b c )\|- b atanh(-----------)
+--R +--------+
+--R | 2
+--R \|b x + a
+--R +
+--R +--------+
+--R +---+ | 2 +---+ +-+
+--R 3 2 2 2 2 +-+ \|- b \|b x + a - \|- b \|a
+--R (2a d - 8a b c d + 16a b c )\|b atan(------------------------------)
+--R b x
+--R /
+--R 2 +---+ +-+
+--R 16b \|- b \|b
+--R Type: Expression(Integer)
+--E 291
+
+--S 292 of 994
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 292
+
+)clear all
+
+--S 293 of 994
+t0:=(a+b*x^2)^(1/2)*(c+d*x^2)
+--R
+--R
+--R +--------+
+--R 2 | 2
+--R (1) (d x + c)\|b x + a
+--R Type: Expression(Integer)
+--E 293
+
+--S 294 of 994
+r0:=1/4*d*x*(a+b*x^2)^(3/2)/b+1/8*a*(4*b*c-a*d)*atanh(x*sqrt(b)/_
+ sqrt(a+b*x^2))/b^(3/2)+1/8*(4*b*c-a*d)*x*sqrt(a+b*x^2)/b
+--R
+--R
+--R (2)
+--R +-+ +--------+
+--R 2 x\|b 3 +-+ | 2
+--R (- a d + 4a b c)atanh(-----------) + (2b d x + (a d + 4b c)x)\|b \|b x + a
+--R +--------+
+--R | 2
+--R \|b x + a
+--R -----------------------------------------------------------------------------
+--R +-+
+--R 8b\|b
+--R Type: Expression(Integer)
+--E 294
+
+--S 295 of 994
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R +--------+
+--R 2 2 2 3 2 +-+ | 2
+--R ((4a b d - 16a b c)x + 8a d - 32a b c)\|a \|b x + a
+--R +
+--R 2 2 3 4 3 2 2 2 4 3
+--R (- a b d + 4a b c)x + (- 8a b d + 32a b c)x - 8a d + 32a b c
+--R *
+--R +--------+
+--R +-+ +-+ | 2 2 +-+ +-+
+--R (\|a \|b + b x)\|b x + a + (- b x - a)\|b - b x\|a
+--R log(--------------------------------------------------------)
+--R +--------+
+--R +-+ | 2
+--R \|a \|b x + a - a
+--R +
+--R 3 7 2 3 5 2 2 3
+--R - 2b d x + (- 17a b d - 4b c)x + (- 24a b d - 32a b c)x
+--R +
+--R 3 2
+--R (- 8a d - 32a b c)x
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|b \|b x + a
+--R +
+--R 3 7 2 3 5 2 2 3
+--R 8b d x + (28a b d + 16b c)x + (28a b d + 48a b c)x
+--R +
+--R 3 2
+--R (8a d + 32a b c)x
+--R *
+--R +-+ +-+
+--R \|a \|b
+--R /
+--R +--------+
+--R 2 2 +-+ +-+ | 2 3 4 2 2 2 +-+
+--R (32b x + 64a b)\|a \|b \|b x + a + (- 8b x - 64a b x - 64a b)\|b
+--R ,
+--R
+--R +--------+
+--R 2 2 2 3 2 +-+ | 2
+--R ((- 8a b d + 32a b c)x - 16a d + 64a b c)\|a \|b x + a
+--R +
+--R 2 2 3 4 3 2 2 2 4 3
+--R (2a b d - 8a b c)x + (16a b d - 64a b c)x + 16a d - 64a b c
+--R *
+--R +--------+
+--R +---+ | 2 +---+ +-+
+--R \|- b \|b x + a - \|- b \|a
+--R atan(------------------------------)
+--R b x
+--R +
+--R 3 7 2 3 5 2 2 3
+--R - 2b d x + (- 17a b d - 4b c)x + (- 24a b d - 32a b c)x
+--R +
+--R 3 2
+--R (- 8a d - 32a b c)x
+--R *
+--R +--------+
+--R +---+ | 2
+--R \|- b \|b x + a
+--R +
+--R 3 7 2 3 5 2 2 3
+--R 8b d x + (28a b d + 16b c)x + (28a b d + 48a b c)x
+--R +
+--R 3 2
+--R (8a d + 32a b c)x
+--R *
+--R +---+ +-+
+--R \|- b \|a
+--R /
+--R +--------+
+--R 2 2 +---+ +-+ | 2
+--R (32b x + 64a b)\|- b \|a \|b x + a
+--R +
+--R 3 4 2 2 2 +---+
+--R (- 8b x - 64a b x - 64a b)\|- b
+--R ]
+--R Type: Union(List(Expression(Integer)),...)
+--E 295
+
+--S 296 of 994
+m0a:=a0.1-r0
+--R
+--R
+--R (4)
+--R 2
+--R (a d - 4a b c)
+--R *
+--R +--------+
+--R +-+ +-+ | 2 2 +-+ +-+
+--R (\|a \|b + b x)\|b x + a + (- b x - a)\|b - b x\|a
+--R log(--------------------------------------------------------)
+--R +--------+
+--R +-+ | 2
+--R \|a \|b x + a - a
+--R +
+--R +-+
+--R 2 x\|b
+--R (a d - 4a b c)atanh(-----------)
+--R +--------+
+--R | 2
+--R \|b x + a
+--R /
+--R +-+
+--R 8b\|b
+--R Type: Expression(Integer)
+--E 296
+
+--S 297 of 994
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 297
+
+--S 298 of 994
+m0b:=a0.2-r0
+--R
+--R
+--R (6)
+--R +-+
+--R 2 +---+ x\|b
+--R (a d - 4a b c)\|- b atanh(-----------)
+--R +--------+
+--R | 2
+--R \|b x + a
+--R +
+--R +--------+
+--R +---+ | 2 +---+ +-+
+--R 2 +-+ \|- b \|b x + a - \|- b \|a
+--R (- 2a d + 8a b c)\|b atan(------------------------------)
+--R b x
+--R /
+--R +---+ +-+
+--R 8b\|- b \|b
+--R Type: Expression(Integer)
+--E 298
+
+--S 299 of 994
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 299
+
+)clear all
+
+--S 300 of 994
+t0:=(a+b*x^2)^(1/2)
+--R
+--R
+--R +--------+
+--R | 2
+--R (1) \|b x + a
+--R Type: Expression(Integer)
+--E 300
+
+--S 301 of 994
+r0:=1/2*a*atanh(x*sqrt(b)/sqrt(a+b*x^2))/sqrt(b)+1/2*x*sqrt(a+b*x^2)
+--R
+--R
+--R +-+ +--------+
+--R x\|b +-+ | 2
+--R a atanh(-----------) + x\|b \|b x + a
+--R +--------+
+--R | 2
+--R \|b x + a
+--R (2) ---------------------------------------
+--R +-+
+--R 2\|b
+--R Type: Expression(Integer)
+--E 301
+
+--S 302 of 994
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R +--------+
+--R +-+ | 2 2 2
+--R (2a\|a \|b x + a - a b x - 2a )
+--R *
+--R +--------+
+--R +-+ +-+ | 2 2 +-+ +-+
+--R (\|a \|b - b x)\|b x + a + (- b x - a)\|b + b x\|a
+--R log(--------------------------------------------------------)
+--R +--------+
+--R +-+ | 2
+--R \|a \|b x + a - a
+--R +
+--R +--------+
+--R 3 +-+ | 2 3 +-+ +-+
+--R (- b x - 2a x)\|b \|b x + a + (2b x + 2a x)\|a \|b
+--R /
+--R +--------+
+--R +-+ +-+ | 2 2 +-+
+--R 4\|a \|b \|b x + a + (- 2b x - 4a)\|b
+--R ,
+--R
+--R +--------+
+--R +--------+ +---+ | 2 +---+ +-+
+--R +-+ | 2 2 2 \|- b \|b x + a - \|- b \|a
+--R (4a\|a \|b x + a - 2a b x - 4a )atan(------------------------------)
+--R b x
+--R +
+--R +--------+
+--R 3 +---+ | 2 3 +---+ +-+
+--R (- b x - 2a x)\|- b \|b x + a + (2b x + 2a x)\|- b \|a
+--R /
+--R +--------+
+--R +---+ +-+ | 2 2 +---+
+--R 4\|- b \|a \|b x + a + (- 2b x - 4a)\|- b
+--R ]
+--R Type: Union(List(Expression(Integer)),...)
+--E 302
+
+--S 303 of 994
+m0a:=a0.1-r0
+--R
+--R
+--R (4)
+--R +--------+
+--R +-+ +-+ | 2 2 +-+ +-+
+--R (\|a \|b - b x)\|b x + a + (- b x - a)\|b + b x\|a
+--R a log(--------------------------------------------------------)
+--R +--------+
+--R +-+ | 2
+--R \|a \|b x + a - a
+--R +
+--R +-+
+--R x\|b
+--R - a atanh(-----------)
+--R +--------+
+--R | 2
+--R \|b x + a
+--R /
+--R +-+
+--R 2\|b
+--R Type: Expression(Integer)
+--E 303
+
+--S 304 of 994
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 304
+
+--S 305 of 994
+m0b:=a0.2-r0
+--R
+--R
+--R (6)
+--R +--------+
+--R +-+ +---+ | 2 +---+ +-+
+--R +---+ x\|b +-+ \|- b \|b x + a - \|- b \|a
+--R - a\|- b atanh(-----------) + 2a\|b atan(------------------------------)
+--R +--------+ b x
+--R | 2
+--R \|b x + a
+--R ------------------------------------------------------------------------
+--R +---+ +-+
+--R 2\|- b \|b
+--R Type: Expression(Integer)
+--E 305
+
+--S 306 of 994
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 306
+
+)clear all
+
+--S 307 of 994
+t0:=(a+b*x^2)^(1/2)/(c+d*x^2)
+--R
+--R
+--R +--------+
+--R | 2
+--R \|b x + a
+--R (1) -----------
+--R 2
+--R d x + c
+--R Type: Expression(Integer)
+--E 307
+
+--S 308 of 994
+r0:=atanh(x*sqrt(b)/sqrt(a+b*x^2))*sqrt(b)/d-atanh(x*sqrt(b*c-a*d)/_
+ (sqrt(c)*sqrt(a+b*x^2)))*sqrt(b*c-a*d)/(d*sqrt(c))
+--R
+--R
+--R +-+ +-----------+
+--R +-+ +-+ x\|b +-----------+ x\|- a d + b c
+--R \|b \|c atanh(-----------) - \|- a d + b c atanh(---------------)
+--R +--------+ +--------+
+--R | 2 +-+ | 2
+--R \|b x + a \|c \|b x + a
+--R (2) -----------------------------------------------------------------
+--R +-+
+--R d\|c
+--R Type: Expression(Integer)
+--E 308
+
+--S 309 of 994
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R +-----------+
+--R |- a d + b c
+--R |-----------
+--R \| c
+--R *
+--R log
+--R 2 +-+
+--R ((- 2a d + 4b c)x + 2a c)\|a
+--R +
+--R +-----------+
+--R 3 |- a d + b c
+--R (2b c x + 4a c x) |-----------
+--R \| c
+--R *
+--R +--------+
+--R | 2
+--R \|b x + a
+--R +
+--R +-----------+
+--R 3 |- a d + b c +-+ 2 4
+--R (- 4b c x - 4a c x) |----------- \|a + (a b d - 2b c)x
+--R \| c
+--R +
+--R 2 2 2
+--R (2a d - 5a b c)x - 2a c
+--R /
+--R +--------+
+--R 2 +-+ | 2 4 2
+--R (2d x + 2c)\|a \|b x + a - b d x + (- 2a d - b c)x - 2a c
+--R +
+--R +--------+
+--R +-+ +-+ | 2 +-+ +-+ 2
+--R +-+ (- x\|b + \|a )\|b x + a + x\|a \|b - b x - a
+--R 2\|b log(--------------------------------------------------)
+--R +--------+
+--R +-+ | 2
+--R \|a \|b x + a - a
+--R /
+--R 2d
+--R ,
+--R
+--R +--------+
+--R +-+ +-+ | 2 +-+ +-+ 2
+--R +-+ (- x\|b + \|a )\|b x + a + x\|a \|b - b x - a
+--R \|b log(--------------------------------------------------)
+--R +--------+
+--R +-+ | 2
+--R \|a \|b x + a - a
+--R +
+--R +---------+
+--R |a d - b c
+--R |---------
+--R \| c
+--R *
+--R +--------+
+--R 2 | 2 2 +-+
+--R ((a d - b c)x + a c)\|b x + a + (- a d x - a c)\|a
+--R atan(-------------------------------------------------------)
+--R +---------+
+--R 3 |a d - b c
+--R b c x |---------
+--R \| c
+--R +
+--R +---------+ +-+
+--R |a d - b c \|a
+--R |--------- atan(-------------)
+--R \| c +---------+
+--R |a d - b c
+--R x |---------
+--R \| c
+--R /
+--R d
+--R ,
+--R
+--R +-----------+
+--R |- a d + b c
+--R |-----------
+--R \| c
+--R *
+--R log
+--R 2 +-+
+--R ((- 2a d + 4b c)x + 2a c)\|a
+--R +
+--R +-----------+
+--R 3 |- a d + b c
+--R (2b c x + 4a c x) |-----------
+--R \| c
+--R *
+--R +--------+
+--R | 2
+--R \|b x + a
+--R +
+--R +-----------+
+--R 3 |- a d + b c +-+ 2 4
+--R (- 4b c x - 4a c x) |----------- \|a + (a b d - 2b c)x
+--R \| c
+--R +
+--R 2 2 2
+--R (2a d - 5a b c)x - 2a c
+--R /
+--R +--------+
+--R 2 +-+ | 2 4 2
+--R (2d x + 2c)\|a \|b x + a - b d x + (- 2a d - b c)x - 2a c
+--R +
+--R +--------+
+--R | 2 +-+
+--R +---+ \|b x + a - \|a
+--R 4\|- b atan(------------------)
+--R +---+
+--R x\|- b
+--R /
+--R 2d
+--R ,
+--R
+--R +--------+
+--R | 2 +-+
+--R +---+ \|b x + a - \|a
+--R 2\|- b atan(------------------)
+--R +---+
+--R x\|- b
+--R +
+--R +---------+
+--R |a d - b c
+--R |---------
+--R \| c
+--R *
+--R +--------+
+--R 2 | 2 2 +-+
+--R ((a d - b c)x + a c)\|b x + a + (- a d x - a c)\|a
+--R atan(-------------------------------------------------------)
+--R +---------+
+--R 3 |a d - b c
+--R b c x |---------
+--R \| c
+--R +
+--R +---------+ +-+
+--R |a d - b c \|a
+--R |--------- atan(-------------)
+--R \| c +---------+
+--R |a d - b c
+--R x |---------
+--R \| c
+--R /
+--R d
+--R ]
+--R Type: Union(List(Expression(Integer)),...)
+--E 309
+
+--S 310 of 994
+m0a:=a0.1-r0
+--R
+--R
+--R (4)
+--R +-----------+
+--R |- a d + b c +-+
+--R |----------- \|c
+--R \| c
+--R *
+--R log
+--R 2 +-+
+--R ((- 2a d + 4b c)x + 2a c)\|a
+--R +
+--R +-----------+
+--R 3 |- a d + b c
+--R (2b c x + 4a c x) |-----------
+--R \| c
+--R *
+--R +--------+
+--R | 2
+--R \|b x + a
+--R +
+--R +-----------+
+--R 3 |- a d + b c +-+ 2 4
+--R (- 4b c x - 4a c x) |----------- \|a + (a b d - 2b c)x
+--R \| c
+--R +
+--R 2 2 2
+--R (2a d - 5a b c)x - 2a c
+--R /
+--R +--------+
+--R 2 +-+ | 2 4 2
+--R (2d x + 2c)\|a \|b x + a - b d x + (- 2a d - b c)x - 2a c
+--R +
+--R +--------+
+--R +-+ +-+ | 2 +-+ +-+ 2
+--R +-+ +-+ (- x\|b + \|a )\|b x + a + x\|a \|b - b x - a
+--R 2\|b \|c log(--------------------------------------------------)
+--R +--------+
+--R +-+ | 2
+--R \|a \|b x + a - a
+--R +
+--R +-+ +-----------+
+--R +-+ +-+ x\|b +-----------+ x\|- a d + b c
+--R - 2\|b \|c atanh(-----------) + 2\|- a d + b c atanh(---------------)
+--R +--------+ +--------+
+--R | 2 +-+ | 2
+--R \|b x + a \|c \|b x + a
+--R /
+--R +-+
+--R 2d\|c
+--R Type: Expression(Integer)
+--E 310
+
+--S 311 of 994
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 311
+
+--S 312 of 994
+m0b:=a0.2-r0
+--R
+--R
+--R (6)
+--R +--------+
+--R +-+ +-+ | 2 +-+ +-+ 2
+--R +-+ +-+ (- x\|b + \|a )\|b x + a + x\|a \|b - b x - a
+--R \|b \|c log(--------------------------------------------------)
+--R +--------+
+--R +-+ | 2
+--R \|a \|b x + a - a
+--R +
+--R +-+ +-----------+
+--R +-+ +-+ x\|b +-----------+ x\|- a d + b c
+--R - \|b \|c atanh(-----------) + \|- a d + b c atanh(---------------)
+--R +--------+ +--------+
+--R | 2 +-+ | 2
+--R \|b x + a \|c \|b x + a
+--R +
+--R +---------+
+--R +-+ |a d - b c
+--R \|c |---------
+--R \| c
+--R *
+--R +--------+
+--R 2 | 2 2 +-+
+--R ((a d - b c)x + a c)\|b x + a + (- a d x - a c)\|a
+--R atan(-------------------------------------------------------)
+--R +---------+
+--R 3 |a d - b c
+--R b c x |---------
+--R \| c
+--R +
+--R +---------+ +-+
+--R +-+ |a d - b c \|a
+--R \|c |--------- atan(-------------)
+--R \| c +---------+
+--R |a d - b c
+--R x |---------
+--R \| c
+--R /
+--R +-+
+--R d\|c
+--R Type: Expression(Integer)
+--E 312
+
+--S 313 of 994
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 313
+
+)clear all
+
+--S 314 of 994
+t0:=(a+b*x^2)^(1/2)/(c+d*x^2)^2
+--R
+--R
+--R +--------+
+--R | 2
+--R \|b x + a
+--R (1) -------------------
+--R 2 4 2 2
+--R d x + 2c d x + c
+--R Type: Expression(Integer)
+--E 314
+
+--S 315 of 994
+r0:=1/2*a*atanh(x*sqrt(b*c-a*d)/(sqrt(c)*sqrt(a+b*x^2)))/(c^(3/2)*_
+ sqrt(b*c-a*d))+1/2*x*sqrt(a+b*x^2)/(c*(c+d*x^2))
+--R
+--R
+--R +-----------+ +--------+
+--R 2 x\|- a d + b c +-----------+ +-+ | 2
+--R (a d x + a c)atanh(---------------) + x\|- a d + b c \|c \|b x + a
+--R +--------+
+--R +-+ | 2
+--R \|c \|b x + a
+--R (2) ---------------------------------------------------------------------
+--R 2 2 +-----------+ +-+
+--R (2c d x + 2c )\|- a d + b c \|c
+--R Type: Expression(Integer)
+--E 315
+
+--S 316 of 994
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R +--------+
+--R 2 +-+ | 2 4 2 2
+--R (2a d x + 2a c)\|a \|b x + a - a b d x + (- 2a d - a b c)x
+--R +
+--R 2
+--R - 2a c
+--R *
+--R log
+--R +--------------+
+--R 2 | 2 +-+
+--R ((- 2a d + 4b c)x + 2a c)\|- a c d + b c \|a
+--R +
+--R 2 2 3 2 2
+--R (2a b c d - 2b c )x + (4a c d - 4a b c )x
+--R *
+--R +--------+
+--R | 2
+--R \|b x + a
+--R +
+--R 2 2 3 2 2 +-+
+--R ((- 4a b c d + 4b c )x + (- 4a c d + 4a b c )x)\|a
+--R +
+--R +--------------+
+--R 2 4 2 2 2 | 2
+--R ((a b d - 2b c)x + (2a d - 5a b c)x - 2a c)\|- a c d + b c
+--R /
+--R +--------+
+--R 2 +-+ | 2 4 2
+--R (2d x + 2c)\|a \|b x + a - b d x + (- 2a d - b c)x - 2a c
+--R +
+--R +--------------+ +--------+
+--R 3 | 2 | 2
+--R (- 2b x - 4a x)\|- a c d + b c \|b x + a
+--R +
+--R +--------------+
+--R 3 | 2 +-+
+--R (4b x + 4a x)\|- a c d + b c \|a
+--R /
+--R +--------------+ +--------+
+--R 2 2 | 2 +-+ | 2
+--R (8c d x + 8c )\|- a c d + b c \|a \|b x + a
+--R +
+--R +--------------+
+--R 4 2 2 2 | 2
+--R (- 4b c d x + (- 8a c d - 4b c )x - 8a c )\|- a c d + b c
+--R ,
+--R
+--R +--------+
+--R 2 +-+ | 2 4 2 2
+--R (2a d x + 2a c)\|a \|b x + a - a b d x + (- 2a d - a b c)x
+--R +
+--R 2
+--R - 2a c
+--R *
+--R +--------+
+--R 2 | 2 2 +-+
+--R ((a d - b c)x + a c)\|b x + a + (- a d x - a c)\|a
+--R atan(-------------------------------------------------------)
+--R +------------+
+--R 3 | 2
+--R b x \|a c d - b c
+--R +
+--R +--------+
+--R 2 +-+ | 2 4 2 2
+--R (2a d x + 2a c)\|a \|b x + a - a b d x + (- 2a d - a b c)x
+--R +
+--R 2
+--R - 2a c
+--R *
+--R +------------+
+--R +-+ | 2
+--R \|a \|a c d - b c
+--R atan(-------------------)
+--R (a d - b c)x
+--R +
+--R +------------+ +--------+
+--R 3 | 2 | 2
+--R (- b x - 2a x)\|a c d - b c \|b x + a
+--R +
+--R +------------+
+--R 3 +-+ | 2
+--R (2b x + 2a x)\|a \|a c d - b c
+--R /
+--R +------------+ +--------+
+--R 2 2 +-+ | 2 | 2
+--R (4c d x + 4c )\|a \|a c d - b c \|b x + a
+--R +
+--R +------------+
+--R 4 2 2 2 | 2
+--R (- 2b c d x + (- 4a c d - 2b c )x - 4a c )\|a c d - b c
+--R ]
+--R Type: Union(List(Expression(Integer)),...)
+--E 316
+
+--S 317 of 994
+m0a:=a0.1-r0
+--R
+--R
+--R (4)
+--R +-----------+ +-+
+--R a\|- a d + b c \|c
+--R *
+--R log
+--R +--------------+
+--R 2 | 2 +-+
+--R ((- 2a d + 4b c)x + 2a c)\|- a c d + b c \|a
+--R +
+--R 2 2 3 2 2
+--R (2a b c d - 2b c )x + (4a c d - 4a b c )x
+--R *
+--R +--------+
+--R | 2
+--R \|b x + a
+--R +
+--R 2 2 3 2 2 +-+
+--R ((- 4a b c d + 4b c )x + (- 4a c d + 4a b c )x)\|a
+--R +
+--R +--------------+
+--R 2 4 2 2 2 | 2
+--R ((a b d - 2b c)x + (2a d - 5a b c)x - 2a c)\|- a c d + b c
+--R /
+--R +--------+
+--R 2 +-+ | 2 4 2
+--R (2d x + 2c)\|a \|b x + a - b d x + (- 2a d - b c)x - 2a c
+--R +
+--R +--------------+ +-----------+
+--R | 2 x\|- a d + b c
+--R - 2a\|- a c d + b c atanh(---------------)
+--R +--------+
+--R +-+ | 2
+--R \|c \|b x + a
+--R /
+--R +--------------+
+--R | 2 +-----------+ +-+
+--R 4c\|- a c d + b c \|- a d + b c \|c
+--R Type: Expression(Integer)
+--E 317
+
+--S 318 of 994
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 318
+
+--S 319 of 994
+m0b:=a0.2-r0
+--R
+--R
+--R (6)
+--R +------------+ +-----------+
+--R | 2 x\|- a d + b c
+--R - a\|a c d - b c atanh(---------------)
+--R +--------+
+--R +-+ | 2
+--R \|c \|b x + a
+--R +
+--R +-----------+ +-+
+--R a\|- a d + b c \|c
+--R *
+--R +--------+
+--R 2 | 2 2 +-+
+--R ((a d - b c)x + a c)\|b x + a + (- a d x - a c)\|a
+--R atan(-------------------------------------------------------)
+--R +------------+
+--R 3 | 2
+--R b x \|a c d - b c
+--R +
+--R +------------+
+--R +-+ | 2
+--R +-----------+ +-+ \|a \|a c d - b c
+--R a\|- a d + b c \|c atan(-------------------)
+--R (a d - b c)x
+--R /
+--R +------------+
+--R +-----------+ +-+ | 2
+--R 2c\|- a d + b c \|c \|a c d - b c
+--R Type: Expression(Integer)
+--E 319
+
+--S 320 of 994
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 320
+
+)clear all
+
+--S 321 of 994
+t0:=(a+b*x^2)^(1/2)/(c+d*x^2)^3
+--R
+--R
+--R +--------+
+--R | 2
+--R \|b x + a
+--R (1) -----------------------------
+--R 3 6 2 4 2 2 3
+--R d x + 3c d x + 3c d x + c
+--R Type: Expression(Integer)
+--E 321
+
+--S 322 of 994
+r0:=1/8*a*(4*b*c-3*a*d)*atanh(x*sqrt(b*c-a*d)/(sqrt(c)*sqrt(a+b*x^2)))/_
+ (c^(5/2)*(b*c-a*d)^(3/2))+1/4*x*sqrt(a+b*x^2)/(c*(c+d*x^2)^2)+_
+ 1/8*(2*b*c-3*a*d)*x*sqrt(a+b*x^2)/(c^2*(b*c-a*d)*(c+d*x^2))
+--R
+--R
+--R (2)
+--R 2 3 2 4 2 2 2 2 2 2 3
+--R ((3a d - 4a b c d )x + (6a c d - 8a b c d)x + 3a c d - 4a b c )
+--R *
+--R +-----------+
+--R x\|- a d + b c
+--R atanh(---------------)
+--R +--------+
+--R +-+ | 2
+--R \|c \|b x + a
+--R +
+--R +--------+
+--R 2 3 2 +-----------+ +-+ | 2
+--R ((3a d - 2b c d)x + (5a c d - 4b c )x)\|- a d + b c \|c \|b x + a
+--R /
+--R 2 3 3 2 4 3 2 4 2 4 5
+--R ((8a c d - 8b c d )x + (16a c d - 16b c d)x + 8a c d - 8b c )
+--R *
+--R +-----------+ +-+
+--R \|- a d + b c \|c
+--R Type: Expression(Integer)
+--E 322
+
+--S 323 of 994
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R 2 3 2 2 6 3 3 2 2 2 2 4
+--R (12a b d - 16a b c d )x + (24a d - 8a b c d - 32a b c d)x
+--R +
+--R 3 2 2 2 2 3 2 3 2 2 3
+--R (48a c d - 52a b c d - 16a b c )x + 24a c d - 32a b c
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|a \|b x + a
+--R +
+--R 2 2 3 3 2 8 3 3 2 2 2 3 2 6
+--R (- 3a b d + 4a b c d )x + (- 24a b d + 26a b c d + 8a b c d)x
+--R +
+--R 4 3 3 2 2 2 2 3 3 4
+--R (- 24a d - 16a b c d + 61a b c d + 4a b c )x
+--R +
+--R 4 2 3 2 2 2 3 2 4 2 3 3
+--R (- 48a c d + 40a b c d + 32a b c )x - 24a c d + 32a b c
+--R *
+--R log
+--R +--------------+
+--R 2 | 2 +-+
+--R ((- 2a d + 4b c)x + 2a c)\|- a c d + b c \|a
+--R +
+--R 2 2 3 2 2
+--R (2a b c d - 2b c )x + (4a c d - 4a b c )x
+--R *
+--R +--------+
+--R | 2
+--R \|b x + a
+--R +
+--R 2 2 3 2 2 +-+
+--R ((- 4a b c d + 4b c )x + (- 4a c d + 4a b c )x)\|a
+--R +
+--R +--------------+
+--R 2 4 2 2 2 | 2
+--R ((a b d - 2b c)x + (2a d - 5a b c)x - 2a c)\|- a c d + b c
+--R /
+--R +--------+
+--R 2 +-+ | 2 4 2
+--R (2d x + 2c)\|a \|b x + a - b d x + (- 2a d - b c)x - 2a c
+--R +
+--R 2 2 3 7 2 2 2 3 2 5
+--R (- 6a b d + 4b c d)x + (- 48a b d + 22a b c d + 8b c )x
+--R +
+--R 3 2 2 2 2 3 3 2 2
+--R (- 48a d - 48a b c d + 64a b c )x + (- 80a c d + 64a b c )x
+--R *
+--R +--------------+ +--------+
+--R | 2 | 2
+--R \|- a c d + b c \|b x + a
+--R +
+--R 2 2 3 7 2 2 2 3 2 5
+--R (24a b d - 16b c d)x + (72a b d - 8a b c d - 32b c )x
+--R +
+--R 3 2 2 2 2 3 3 2 2
+--R (48a d + 88a b c d - 96a b c )x + (80a c d - 64a b c )x
+--R *
+--R +--------------+
+--R | 2 +-+
+--R \|- a c d + b c \|a
+--R /
+--R 2 3 2 3 2 6 2 2 3 2 4 4
+--R (64a b c d - 64b c d )x + (128a c d - 128b c d)x
+--R +
+--R 2 3 2 4 2 5 2 2 4 5
+--R (256a c d - 192a b c d - 64b c )x + 128a c d - 128a b c
+--R *
+--R +--------------+ +--------+
+--R | 2 +-+ | 2
+--R \|- a c d + b c \|a \|b x + a
+--R +
+--R 2 2 3 3 3 2 8
+--R (- 16a b c d + 16b c d )x
+--R +
+--R 2 2 3 2 3 2 3 4 6
+--R (- 128a b c d + 96a b c d + 32b c d)x
+--R +
+--R 3 2 3 2 3 2 2 4 3 5 4
+--R (- 128a c d - 128a b c d + 240a b c d + 16b c )x
+--R +
+--R 3 3 2 2 4 2 5 2 3 4 2 5
+--R (- 256a c d + 128a b c d + 128a b c )x - 128a c d + 128a b c
+--R *
+--R +--------------+
+--R | 2
+--R \|- a c d + b c
+--R ,
+--R
+--R 2 3 2 2 6 3 3 2 2 2 2 4
+--R (12a b d - 16a b c d )x + (24a d - 8a b c d - 32a b c d)x
+--R +
+--R 3 2 2 2 2 3 2 3 2 2 3
+--R (48a c d - 52a b c d - 16a b c )x + 24a c d - 32a b c
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|a \|b x + a
+--R +
+--R 2 2 3 3 2 8 3 3 2 2 2 3 2 6
+--R (- 3a b d + 4a b c d )x + (- 24a b d + 26a b c d + 8a b c d)x
+--R +
+--R 4 3 3 2 2 2 2 3 3 4
+--R (- 24a d - 16a b c d + 61a b c d + 4a b c )x
+--R +
+--R 4 2 3 2 2 2 3 2 4 2 3 3
+--R (- 48a c d + 40a b c d + 32a b c )x - 24a c d + 32a b c
+--R *
+--R +--------+
+--R 2 | 2 2 +-+
+--R ((a d - b c)x + a c)\|b x + a + (- a d x - a c)\|a
+--R atan(-------------------------------------------------------)
+--R +------------+
+--R 3 | 2
+--R b x \|a c d - b c
+--R +
+--R 2 3 2 2 6 3 3 2 2 2 2 4
+--R (12a b d - 16a b c d )x + (24a d - 8a b c d - 32a b c d)x
+--R +
+--R 3 2 2 2 2 3 2 3 2 2 3
+--R (48a c d - 52a b c d - 16a b c )x + 24a c d - 32a b c
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|a \|b x + a
+--R +
+--R 2 2 3 3 2 8 3 3 2 2 2 3 2 6
+--R (- 3a b d + 4a b c d )x + (- 24a b d + 26a b c d + 8a b c d)x
+--R +
+--R 4 3 3 2 2 2 2 3 3 4
+--R (- 24a d - 16a b c d + 61a b c d + 4a b c )x
+--R +
+--R 4 2 3 2 2 2 3 2 4 2 3 3
+--R (- 48a c d + 40a b c d + 32a b c )x - 24a c d + 32a b c
+--R *
+--R +------------+
+--R +-+ | 2
+--R \|a \|a c d - b c
+--R atan(-------------------)
+--R (a d - b c)x
+--R +
+--R 2 2 3 7 2 2 2 3 2 5
+--R (- 3a b d + 2b c d)x + (- 24a b d + 11a b c d + 4b c )x
+--R +
+--R 3 2 2 2 2 3 3 2 2
+--R (- 24a d - 24a b c d + 32a b c )x + (- 40a c d + 32a b c )x
+--R *
+--R +------------+ +--------+
+--R | 2 | 2
+--R \|a c d - b c \|b x + a
+--R +
+--R 2 2 3 7 2 2 2 3 2 5
+--R (12a b d - 8b c d)x + (36a b d - 4a b c d - 16b c )x
+--R +
+--R 3 2 2 2 2 3 3 2 2
+--R (24a d + 44a b c d - 48a b c )x + (40a c d - 32a b c )x
+--R *
+--R +------------+
+--R +-+ | 2
+--R \|a \|a c d - b c
+--R /
+--R 2 3 2 3 2 6 2 2 3 2 4 4
+--R (32a b c d - 32b c d )x + (64a c d - 64b c d)x
+--R +
+--R 2 3 2 4 2 5 2 2 4 5
+--R (128a c d - 96a b c d - 32b c )x + 64a c d - 64a b c
+--R *
+--R +------------+ +--------+
+--R +-+ | 2 | 2
+--R \|a \|a c d - b c \|b x + a
+--R +
+--R 2 2 3 3 3 2 8 2 2 3 2 3 2 3 4 6
+--R (- 8a b c d + 8b c d )x + (- 64a b c d + 48a b c d + 16b c d)x
+--R +
+--R 3 2 3 2 3 2 2 4 3 5 4
+--R (- 64a c d - 64a b c d + 120a b c d + 8b c )x
+--R +
+--R 3 3 2 2 4 2 5 2 3 4 2 5
+--R (- 128a c d + 64a b c d + 64a b c )x - 64a c d + 64a b c
+--R *
+--R +------------+
+--R | 2
+--R \|a c d - b c
+--R ]
+--R Type: Union(List(Expression(Integer)),...)
+--E 323
+
+--S 324 of 994
+m0a:=a0.1-r0
+--R
+--R
+--R (4)
+--R 2 +-----------+ +-+
+--R (3a d - 4a b c)\|- a d + b c \|c
+--R *
+--R log
+--R +--------------+
+--R 2 | 2 +-+
+--R ((- 2a d + 4b c)x + 2a c)\|- a c d + b c \|a
+--R +
+--R 2 2 3 2 2
+--R (2a b c d - 2b c )x + (4a c d - 4a b c )x
+--R *
+--R +--------+
+--R | 2
+--R \|b x + a
+--R +
+--R 2 2 3 2 2 +-+
+--R ((- 4a b c d + 4b c )x + (- 4a c d + 4a b c )x)\|a
+--R +
+--R +--------------+
+--R 2 4 2 2 2 | 2
+--R ((a b d - 2b c)x + (2a d - 5a b c)x - 2a c)\|- a c d + b c
+--R /
+--R +--------+
+--R 2 +-+ | 2 4 2
+--R (2d x + 2c)\|a \|b x + a - b d x + (- 2a d - b c)x - 2a c
+--R +
+--R +--------------+ +-----------+
+--R 2 | 2 x\|- a d + b c
+--R (- 6a d + 8a b c)\|- a c d + b c atanh(---------------)
+--R +--------+
+--R +-+ | 2
+--R \|c \|b x + a
+--R /
+--R +--------------+
+--R 2 3 | 2 +-----------+ +-+
+--R (16a c d - 16b c )\|- a c d + b c \|- a d + b c \|c
+--R Type: Expression(Integer)
+--E 324
+
+--S 325 of 994
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 325
+
+--S 326 of 994
+m0b:=a0.2-r0
+--R
+--R
+--R (6)
+--R +------------+ +-----------+
+--R 2 | 2 x\|- a d + b c
+--R (- 3a d + 4a b c)\|a c d - b c atanh(---------------)
+--R +--------+
+--R +-+ | 2
+--R \|c \|b x + a
+--R +
+--R 2 +-----------+ +-+
+--R (3a d - 4a b c)\|- a d + b c \|c
+--R *
+--R +--------+
+--R 2 | 2 2 +-+
+--R ((a d - b c)x + a c)\|b x + a + (- a d x - a c)\|a
+--R atan(-------------------------------------------------------)
+--R +------------+
+--R 3 | 2
+--R b x \|a c d - b c
+--R +
+--R +------------+
+--R +-+ | 2
+--R 2 +-----------+ +-+ \|a \|a c d - b c
+--R (3a d - 4a b c)\|- a d + b c \|c atan(-------------------)
+--R (a d - b c)x
+--R /
+--R +------------+
+--R 2 3 +-----------+ +-+ | 2
+--R (8a c d - 8b c )\|- a d + b c \|c \|a c d - b c
+--R Type: Expression(Integer)
+--E 326
+
+--S 327 of 994
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 327
+
+)clear all
+
+--S 328 of 994
+t0:=(a+b*x^2)^(1/2)/(c+d*x^2)^4
+--R
+--R
+--R +--------+
+--R | 2
+--R \|b x + a
+--R (1) ---------------------------------------
+--R 4 8 3 6 2 2 4 3 2 4
+--R d x + 4c d x + 6c d x + 4c d x + c
+--R Type: Expression(Integer)
+--E 328
+
+--S 329 of 994
+r0:=1/16*a*(8*b^2*c^2-12*a*b*c*d+5*a^2*d^2)*atanh(x*sqrt(b*c-a*d)/_
+ (sqrt(c)*sqrt(a+b*x^2)))/(c^(7/2)*(b*c-a*d)^(5/2))+1/6*x*_
+ sqrt(a+b*x^2)/(c*(c+d*x^2)^3)+1/24*(4*b*c-5*a*d)*x*sqrt(a+_
+ b*x^2)/(c^2*(b*c-a*d)*(c+d*x^2)^2)+1/48*(2*b*c-5*a*d)*(4*b*c-_
+ 3*a*d)*x*sqrt(a+b*x^2)/(c^3*(b*c-a*d)^2*(c+d*x^2))
+--R
+--R
+--R (2)
+--R 3 5 2 4 2 2 3 6
+--R (15a d - 36a b c d + 24a b c d )x
+--R +
+--R 3 4 2 2 3 2 3 2 4
+--R (45a c d - 108a b c d + 72a b c d )x
+--R +
+--R 3 2 3 2 3 2 2 4 2 3 3 2 2 4
+--R (45a c d - 108a b c d + 72a b c d)x + 15a c d - 36a b c d
+--R +
+--R 2 5
+--R 24a b c
+--R *
+--R +-----------+
+--R x\|- a d + b c
+--R atanh(---------------)
+--R +--------+
+--R +-+ | 2
+--R \|c \|b x + a
+--R +
+--R 2 4 3 2 2 2 5
+--R (15a d - 26a b c d + 8b c d )x
+--R +
+--R 2 3 2 2 2 3 3 2 2 2 3 2 4
+--R (40a c d - 70a b c d + 24b c d)x + (33a c d - 60a b c d + 24b c )x
+--R *
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+--R +-----------+ +-+ | 2
+--R \|- a d + b c \|c \|b x + a
+--R /
+--R 2 3 5 4 4 2 5 3 6
+--R (48a c d - 96a b c d + 48b c d )x
+--R +
+--R 2 4 4 5 3 2 6 2 4
+--R (144a c d - 288a b c d + 144b c d )x
+--R +
+--R 2 5 3 6 2 2 7 2 2 6 2 7 2 8
+--R (144a c d - 288a b c d + 144b c d)x + 48a c d - 96a b c d + 48b c
+--R *
+--R +-----------+ +-+
+--R \|- a d + b c \|c
+--R Type: Expression(Integer)
+--E 329
+
+--S 330 of 994
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R 3 2 5 2 3 4 4 2 3 10
+--R (90a b d - 216a b c d + 144a b c d )x
+--R +
+--R 4 5 3 2 4 2 3 2 3 4 3 2 8
+--R (480a b d - 882a b c d + 120a b c d + 432a b c d )x
+--R +
+--R 5 5 4 4 3 2 2 3 2 3 3 2
+--R 480a d + 288a b c d - 2418a b c d + 1656a b c d
+--R +
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+--R 432a b c d
+--R *
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+--R x
+--R +
+--R 5 4 4 2 3 3 2 3 2 2 3 4
+--R 1440a c d - 2016a b c d - 1062a b c d + 2088a b c d
+--R +
+--R 4 5
+--R 144a b c
+--R *
+--R 4
+--R x
+--R +
+--R 5 2 3 4 3 2 3 2 4 2 3 5 2
+--R (1440a c d - 2976a b c d + 1152a b c d + 768a b c )x
+--R +
+--R 5 3 2 4 4 3 2 5
+--R 480a c d - 1152a b c d + 768a b c
+--R *
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+--R +-+ | 2
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+--R +
+--R 3 3 5 2 4 4 5 2 3 12
+--R (- 15a b d + 36a b c d - 24a b c d )x
+--R +
+--R 4 2 5 3 3 4 2 4 2 3 5 3 2 10
+--R (- 270a b d + 603a b c d - 324a b c d - 72a b c d )x
+--R +
+--R 5 5 4 2 4 3 3 2 3 2 4 3 2
+--R - 720a b d + 918a b c d + 747a b c d - 1188a b c d
+--R +
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+--R - 72a b c d
+--R *
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+--R x
+--R +
+--R 6 5 5 4 4 2 2 3 3 3 3 2
+--R - 480a d - 1008a b c d + 3606a b c d - 1527a b c d
+--R +
+--R 2 4 4 5 5
+--R - 1260a b c d - 24a b c
+--R *
+--R 6
+--R x
+--R +
+--R 6 4 5 2 3 4 2 3 2 3 3 4
+--R - 1440a c d + 1296a b c d + 2610a b c d - 2808a b c d
+--R +
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+--R - 432a b c
+--R *
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+--R x
+--R +
+--R 6 2 3 5 3 2 4 2 4 3 3 5 2
+--R (- 1440a c d + 2736a b c d - 576a b c d - 1152a b c )x
+--R +
+--R 6 3 2 5 4 4 2 5
+--R - 480a c d + 1152a b c d - 768a b c
+--R *
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+--R 2 | 2 +-+
+--R ((- 2a d + 4b c)x + 2a c)\|- a c d + b c \|a
+--R +
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+--R (2a b c d - 2b c )x + (4a c d - 4a b c )x
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+--R 2 2 3 2 2 +-+
+--R ((- 4a b c d + 4b c )x + (- 4a c d + 4a b c )x)\|a
+--R +
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+--R 2 4 2 2 2 | 2
+--R ((a b d - 2b c)x + (2a d - 5a b c)x - 2a c)\|- a c d + b c
+--R /
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+--R 2 +-+ | 2 4 2
+--R (2d x + 2c)\|a \|b x + a - b d x + (- 2a d - b c)x - 2a c
+--R +
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+--R (- 30a b d + 52a b c d - 16b c d )x
+--R +
+--R 3 2 4 2 3 3 4 2 2 5 3 9
+--R (- 540a b d + 856a b c d - 148a b c d - 48b c d)x
+--R +
+--R 4 4 3 2 3 2 3 2 2 4 3
+--R - 1440a b d + 1056a b c d + 1686a b c d - 744a b c d
+--R +
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+--R - 48b c
+--R *
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+--R x
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+--R 5 4 4 3 3 2 2 2 2 3 3
+--R - 960a d - 2176a b c d + 5020a b c d - 144a b c d
+--R +
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+--R - 864a b c
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+--R x
+--R +
+--R 5 3 4 2 2 3 2 3 2 3 4 3
+--R (- 2560a c d + 1312a b c d + 4224a b c d - 2304a b c )x
+--R +
+--R 5 2 2 4 3 3 2 4
+--R (- 2112a c d + 3840a b c d - 1536a b c )x
+--R *
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+--R \|- a c d + b c \|b x + a
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+--R (180a b d - 312a b c d + 96b c d )x
+--R +
+--R 3 2 4 2 3 3 4 2 2 5 3 9
+--R (1140a b d - 1496a b c d - 232a b c d + 288b c d)x
+--R +
+--R 4 4 3 2 3 2 3 2 2 4 3 5 4 7
+--R (1920a b d - 288a b c d - 3900a b c d + 1104a b c d + 288b c )x
+--R +
+--R 5 4 4 3 3 2 2 2 2 3 3
+--R 960a d + 3456a b c d - 5940a b c d - 1488a b c d
+--R +
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+--R 1824a b c
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+--R 5
+--R x
+--R +
+--R 5 3 4 2 2 3 2 3 2 3 4 3
+--R (2560a c d - 256a b c d - 6144a b c d + 3072a b c )x
+--R +
+--R 5 2 2 4 3 3 2 4
+--R (2112a c d - 3840a b c d + 1536a b c )x
+--R *
+--R +--------------+
+--R | 2 +-+
+--R \|- a c d + b c \|a
+--R /
+--R 2 2 3 5 3 4 4 4 5 3 10
+--R (576a b c d - 1152a b c d + 576b c d )x
+--R +
+--R 3 3 5 2 2 4 4 3 5 3 4 6 2 8
+--R (3072a b c d - 4416a b c d - 384a b c d + 1728b c d )x
+--R +
+--R 4 3 5 3 4 4 2 2 5 3 3 6 2
+--R 3072a c d + 3072a b c d - 13632a b c d + 5760a b c d
+--R +
+--R 4 7
+--R 1728b c d
+--R *
+--R 6
+--R x
+--R +
+--R 4 4 4 3 5 3 2 2 6 2 3 7
+--R 9216a c d - 9216a b c d - 8640a b c d + 8064a b c d
+--R +
+--R 4 8
+--R 576b c
+--R *
+--R 4
+--R x
+--R +
+--R 4 5 3 3 6 2 2 2 7 3 8 2
+--R (9216a c d - 15360a b c d + 3072a b c d + 3072a b c )x
+--R +
+--R 4 6 2 3 7 2 2 8
+--R 3072a c d - 6144a b c d + 3072a b c
+--R *
+--R +--------------+ +--------+
+--R | 2 +-+ | 2
+--R \|- a c d + b c \|a \|b x + a
+--R +
+--R 2 3 3 5 4 4 4 5 5 3 12
+--R (- 96a b c d + 192a b c d - 96b c d )x
+--R +
+--R 3 2 3 5 2 3 4 4 4 5 3 5 6 2 10
+--R (- 1728a b c d + 3168a b c d - 1152a b c d - 288b c d )x
+--R +
+--R 4 3 5 3 2 4 4 2 3 5 3 4 6 2
+--R - 4608a b c d + 4032a b c d + 5472a b c d - 4608a b c d
+--R +
+--R 5 7
+--R - 288b c d
+--R *
+--R 8
+--R x
+--R +
+--R 5 3 5 4 4 4 3 2 5 3 2 3 6 2
+--R - 3072a c d - 7680a b c d + 19392a b c d - 3552a b c d
+--R +
+--R 4 7 5 8
+--R - 4992a b c d - 96b c
+--R *
+--R 6
+--R x
+--R +
+--R 5 4 4 4 5 3 3 2 6 2 2 3 7
+--R - 9216a c d + 4608a b c d + 16704a b c d - 10368a b c d
+--R +
+--R 4 8
+--R - 1728a b c
+--R *
+--R 4
+--R x
+--R +
+--R 5 5 3 4 6 2 2 3 8 2 5 6 2
+--R (- 9216a c d + 13824a b c d - 4608a b c )x - 3072a c d
+--R +
+--R 4 7 3 2 8
+--R 6144a b c d - 3072a b c
+--R *
+--R +--------------+
+--R | 2
+--R \|- a c d + b c
+--R ,
+--R
+--R 3 2 5 2 3 4 4 2 3 10
+--R (90a b d - 216a b c d + 144a b c d )x
+--R +
+--R 4 5 3 2 4 2 3 2 3 4 3 2 8
+--R (480a b d - 882a b c d + 120a b c d + 432a b c d )x
+--R +
+--R 5 5 4 4 3 2 2 3 2 3 3 2
+--R 480a d + 288a b c d - 2418a b c d + 1656a b c d
+--R +
+--R 4 4
+--R 432a b c d
+--R *
+--R 6
+--R x
+--R +
+--R 5 4 4 2 3 3 2 3 2 2 3 4
+--R 1440a c d - 2016a b c d - 1062a b c d + 2088a b c d
+--R +
+--R 4 5
+--R 144a b c
+--R *
+--R 4
+--R x
+--R +
+--R 5 2 3 4 3 2 3 2 4 2 3 5 2
+--R (1440a c d - 2976a b c d + 1152a b c d + 768a b c )x
+--R +
+--R 5 3 2 4 4 3 2 5
+--R 480a c d - 1152a b c d + 768a b c
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|a \|b x + a
+--R +
+--R 3 3 5 2 4 4 5 2 3 12
+--R (- 15a b d + 36a b c d - 24a b c d )x
+--R +
+--R 4 2 5 3 3 4 2 4 2 3 5 3 2 10
+--R (- 270a b d + 603a b c d - 324a b c d - 72a b c d )x
+--R +
+--R 5 5 4 2 4 3 3 2 3 2 4 3 2
+--R - 720a b d + 918a b c d + 747a b c d - 1188a b c d
+--R +
+--R 5 4
+--R - 72a b c d
+--R *
+--R 8
+--R x
+--R +
+--R 6 5 5 4 4 2 2 3 3 3 3 2
+--R - 480a d - 1008a b c d + 3606a b c d - 1527a b c d
+--R +
+--R 2 4 4 5 5
+--R - 1260a b c d - 24a b c
+--R *
+--R 6
+--R x
+--R +
+--R 6 4 5 2 3 4 2 3 2 3 3 4
+--R - 1440a c d + 1296a b c d + 2610a b c d - 2808a b c d
+--R +
+--R 2 4 5
+--R - 432a b c
+--R *
+--R 4
+--R x
+--R +
+--R 6 2 3 5 3 2 4 2 4 3 3 5 2
+--R (- 1440a c d + 2736a b c d - 576a b c d - 1152a b c )x
+--R +
+--R 6 3 2 5 4 4 2 5
+--R - 480a c d + 1152a b c d - 768a b c
+--R *
+--R +--------+
+--R 2 | 2 2 +-+
+--R ((a d - b c)x + a c)\|b x + a + (- a d x - a c)\|a
+--R atan(-------------------------------------------------------)
+--R +------------+
+--R 3 | 2
+--R b x \|a c d - b c
+--R +
+--R 3 2 5 2 3 4 4 2 3 10
+--R (90a b d - 216a b c d + 144a b c d )x
+--R +
+--R 4 5 3 2 4 2 3 2 3 4 3 2 8
+--R (480a b d - 882a b c d + 120a b c d + 432a b c d )x
+--R +
+--R 5 5 4 4 3 2 2 3 2 3 3 2
+--R 480a d + 288a b c d - 2418a b c d + 1656a b c d
+--R +
+--R 4 4
+--R 432a b c d
+--R *
+--R 6
+--R x
+--R +
+--R 5 4 4 2 3 3 2 3 2 2 3 4
+--R 1440a c d - 2016a b c d - 1062a b c d + 2088a b c d
+--R +
+--R 4 5
+--R 144a b c
+--R *
+--R 4
+--R x
+--R +
+--R 5 2 3 4 3 2 3 2 4 2 3 5 2
+--R (1440a c d - 2976a b c d + 1152a b c d + 768a b c )x
+--R +
+--R 5 3 2 4 4 3 2 5
+--R 480a c d - 1152a b c d + 768a b c
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|a \|b x + a
+--R +
+--R 3 3 5 2 4 4 5 2 3 12
+--R (- 15a b d + 36a b c d - 24a b c d )x
+--R +
+--R 4 2 5 3 3 4 2 4 2 3 5 3 2 10
+--R (- 270a b d + 603a b c d - 324a b c d - 72a b c d )x
+--R +
+--R 5 5 4 2 4 3 3 2 3 2 4 3 2
+--R - 720a b d + 918a b c d + 747a b c d - 1188a b c d
+--R +
+--R 5 4
+--R - 72a b c d
+--R *
+--R 8
+--R x
+--R +
+--R 6 5 5 4 4 2 2 3 3 3 3 2
+--R - 480a d - 1008a b c d + 3606a b c d - 1527a b c d
+--R +
+--R 2 4 4 5 5
+--R - 1260a b c d - 24a b c
+--R *
+--R 6
+--R x
+--R +
+--R 6 4 5 2 3 4 2 3 2 3 3 4
+--R - 1440a c d + 1296a b c d + 2610a b c d - 2808a b c d
+--R +
+--R 2 4 5
+--R - 432a b c
+--R *
+--R 4
+--R x
+--R +
+--R 6 2 3 5 3 2 4 2 4 3 3 5 2
+--R (- 1440a c d + 2736a b c d - 576a b c d - 1152a b c )x
+--R +
+--R 6 3 2 5 4 4 2 5
+--R - 480a c d + 1152a b c d - 768a b c
+--R *
+--R +------------+
+--R +-+ | 2
+--R \|a \|a c d - b c
+--R atan(-------------------)
+--R (a d - b c)x
+--R +
+--R 2 3 4 4 3 5 2 2 11
+--R (- 15a b d + 26a b c d - 8b c d )x
+--R +
+--R 3 2 4 2 3 3 4 2 2 5 3 9
+--R (- 270a b d + 428a b c d - 74a b c d - 24b c d)x
+--R +
+--R 4 4 3 2 3 2 3 2 2 4 3 5 4 7
+--R (- 720a b d + 528a b c d + 843a b c d - 372a b c d - 24b c )x
+--R +
+--R 5 4 4 3 3 2 2 2 2 3 3 4 4 5
+--R (- 480a d - 1088a b c d + 2510a b c d - 72a b c d - 432a b c )x
+--R +
+--R 5 3 4 2 2 3 2 3 2 3 4 3
+--R (- 1280a c d + 656a b c d + 2112a b c d - 1152a b c )x
+--R +
+--R 5 2 2 4 3 3 2 4
+--R (- 1056a c d + 1920a b c d - 768a b c )x
+--R *
+--R +------------+ +--------+
+--R | 2 | 2
+--R \|a c d - b c \|b x + a
+--R +
+--R 2 3 4 4 3 5 2 2 11
+--R (90a b d - 156a b c d + 48b c d )x
+--R +
+--R 3 2 4 2 3 3 4 2 2 5 3 9
+--R (570a b d - 748a b c d - 116a b c d + 144b c d)x
+--R +
+--R 4 4 3 2 3 2 3 2 2 4 3 5 4 7
+--R (960a b d - 144a b c d - 1950a b c d + 552a b c d + 144b c )x
+--R +
+--R 5 4 4 3 3 2 2 2 2 3 3 4 4 5
+--R (480a d + 1728a b c d - 2970a b c d - 744a b c d + 912a b c )x
+--R +
+--R 5 3 4 2 2 3 2 3 2 3 4 3
+--R (1280a c d - 128a b c d - 3072a b c d + 1536a b c )x
+--R +
+--R 5 2 2 4 3 3 2 4
+--R (1056a c d - 1920a b c d + 768a b c )x
+--R *
+--R +------------+
+--R +-+ | 2
+--R \|a \|a c d - b c
+--R /
+--R 2 2 3 5 3 4 4 4 5 3 10
+--R (288a b c d - 576a b c d + 288b c d )x
+--R +
+--R 3 3 5 2 2 4 4 3 5 3 4 6 2 8
+--R (1536a b c d - 2208a b c d - 192a b c d + 864b c d )x
+--R +
+--R 4 3 5 3 4 4 2 2 5 3 3 6 2
+--R 1536a c d + 1536a b c d - 6816a b c d + 2880a b c d
+--R +
+--R 4 7
+--R 864b c d
+--R *
+--R 6
+--R x
+--R +
+--R 4 4 4 3 5 3 2 2 6 2 3 7
+--R 4608a c d - 4608a b c d - 4320a b c d + 4032a b c d
+--R +
+--R 4 8
+--R 288b c
+--R *
+--R 4
+--R x
+--R +
+--R 4 5 3 3 6 2 2 2 7 3 8 2
+--R (4608a c d - 7680a b c d + 1536a b c d + 1536a b c )x
+--R +
+--R 4 6 2 3 7 2 2 8
+--R 1536a c d - 3072a b c d + 1536a b c
+--R *
+--R +------------+ +--------+
+--R +-+ | 2 | 2
+--R \|a \|a c d - b c \|b x + a
+--R +
+--R 2 3 3 5 4 4 4 5 5 3 12
+--R (- 48a b c d + 96a b c d - 48b c d )x
+--R +
+--R 3 2 3 5 2 3 4 4 4 5 3 5 6 2 10
+--R (- 864a b c d + 1584a b c d - 576a b c d - 144b c d )x
+--R +
+--R 4 3 5 3 2 4 4 2 3 5 3 4 6 2
+--R - 2304a b c d + 2016a b c d + 2736a b c d - 2304a b c d
+--R +
+--R 5 7
+--R - 144b c d
+--R *
+--R 8
+--R x
+--R +
+--R 5 3 5 4 4 4 3 2 5 3 2 3 6 2
+--R - 1536a c d - 3840a b c d + 9696a b c d - 1776a b c d
+--R +
+--R 4 7 5 8
+--R - 2496a b c d - 48b c
+--R *
+--R 6
+--R x
+--R +
+--R 5 4 4 4 5 3 3 2 6 2 2 3 7
+--R - 4608a c d + 2304a b c d + 8352a b c d - 5184a b c d
+--R +
+--R 4 8
+--R - 864a b c
+--R *
+--R 4
+--R x
+--R +
+--R 5 5 3 4 6 2 2 3 8 2 5 6 2
+--R (- 4608a c d + 6912a b c d - 2304a b c )x - 1536a c d
+--R +
+--R 4 7 3 2 8
+--R 3072a b c d - 1536a b c
+--R *
+--R +------------+
+--R | 2
+--R \|a c d - b c
+--R ]
+--R Type: Union(List(Expression(Integer)),...)
+--E 330
+
+--S 331 of 994
+m0a:=a0.1-r0
+--R
+--R
+--R (4)
+--R 3 2 2 2 2 +-----------+ +-+
+--R (5a d - 12a b c d + 8a b c )\|- a d + b c \|c
+--R *
+--R log
+--R +--------------+
+--R 2 | 2 +-+
+--R ((- 2a d + 4b c)x + 2a c)\|- a c d + b c \|a
+--R +
+--R 2 2 3 2 2
+--R (2a b c d - 2b c )x + (4a c d - 4a b c )x
+--R *
+--R +--------+
+--R | 2
+--R \|b x + a
+--R +
+--R 2 2 3 2 2 +-+
+--R ((- 4a b c d + 4b c )x + (- 4a c d + 4a b c )x)\|a
+--R +
+--R +--------------+
+--R 2 4 2 2 2 | 2
+--R ((a b d - 2b c)x + (2a d - 5a b c)x - 2a c)\|- a c d + b c
+--R /
+--R +--------+
+--R 2 +-+ | 2 4 2
+--R (2d x + 2c)\|a \|b x + a - b d x + (- 2a d - b c)x - 2a c
+--R +
+--R +--------------+ +-----------+
+--R 3 2 2 2 2 | 2 x\|- a d + b c
+--R (- 10a d + 24a b c d - 16a b c )\|- a c d + b c atanh(---------------)
+--R +--------+
+--R +-+ | 2
+--R \|c \|b x + a
+--R /
+--R +--------------+
+--R 2 3 2 4 2 5 | 2 +-----------+ +-+
+--R (32a c d - 64a b c d + 32b c )\|- a c d + b c \|- a d + b c \|c
+--R Type: Expression(Integer)
+--E 331
+
+--S 332 of 994
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 332
+
+--S 333 of 994
+m0b:=a0.2-r0
+--R
+--R
+--R (6)
+--R +------------+ +-----------+
+--R 3 2 2 2 2 | 2 x\|- a d + b c
+--R (- 5a d + 12a b c d - 8a b c )\|a c d - b c atanh(---------------)
+--R +--------+
+--R +-+ | 2
+--R \|c \|b x + a
+--R +
+--R 3 2 2 2 2 +-----------+ +-+
+--R (5a d - 12a b c d + 8a b c )\|- a d + b c \|c
+--R *
+--R +--------+
+--R 2 | 2 2 +-+
+--R ((a d - b c)x + a c)\|b x + a + (- a d x - a c)\|a
+--R atan(-------------------------------------------------------)
+--R +------------+
+--R 3 | 2
+--R b x \|a c d - b c
+--R +
+--R +------------+
+--R +-+ | 2
+--R 3 2 2 2 2 +-----------+ +-+ \|a \|a c d - b c
+--R (5a d - 12a b c d + 8a b c )\|- a d + b c \|c atan(-------------------)
+--R (a d - b c)x
+--R /
+--R +------------+
+--R 2 3 2 4 2 5 +-----------+ +-+ | 2
+--R (16a c d - 32a b c d + 16b c )\|- a d + b c \|c \|a c d - b c
+--R Type: Expression(Integer)
+--E 333
+
+--S 334 of 994
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 334
+
+)clear all
+
+--S 335 of 994
+t0:=(a+b*x^2)^(3/2)*(c+d*x^2)^3
+--R
+--R
+--R (1)
+--R 3 8 3 2 6 2 2 4 2 3 2
+--R b d x + (a d + 3b c d )x + (3a c d + 3b c d)x + (3a c d + b c )x
+--R +
+--R 3
+--R a c
+--R *
+--R +--------+
+--R | 2
+--R \|b x + a
+--R Type: Expression(Integer)
+--E 335
+
+--S 336 of 994
+r0:=1/128*(4*b*c-a*d)*(8*b^2*c^2-2*a*b*c*d+a^2*d^2)*x*(a+b*x^2)^(3/2)/_
+ b^3+1/160*d*(44*b^2*c^2-28*a*b*c*d+5*a^2*d^2)*x*(a+b*x^2)^(5/2)/_
+ b^3+1/10*d*x*(a+b*x^2)^(5/2)*(c+d*x^2)^2/b+1/80*d*x*(a+_
+ b*x^2)^(5/2)*(c*(10*b*c-a*d)+d*(14*b*c-5*a*d)*x^2)/b^2+3/256*_
+ a^2*(4*b*c-a*d)*(8*b^2*c^2-2*a*b*c*d+a^2*d^2)*atanh(x*_
+ sqrt(b)/sqrt(a+b*x^2))/b^(7/2)+3/256*a*(4*b*c-a*d)*(8*b^2*_
+ c^2-2*a*b*c*d+a^2*d^2)*x*sqrt(a+b*x^2)/b^3
+--R
+--R
+--R (2)
+--R +-+
+--R 5 3 4 2 3 2 2 2 3 3 x\|b
+--R (- 15a d + 90a b c d - 240a b c d + 480a b c )atanh(-----------)
+--R +--------+
+--R | 2
+--R \|b x + a
+--R +
+--R 4 3 9 3 3 4 2 7
+--R 128b d x + (176a b d + 480b c d )x
+--R +
+--R 2 2 3 3 2 4 2 5
+--R (8a b d + 720a b c d + 640b c d)x
+--R +
+--R 3 3 2 2 2 3 2 4 3 3
+--R (- 10a b d + 60a b c d + 1120a b c d + 320b c )x
+--R +
+--R 4 3 3 2 2 2 2 3 3
+--R (15a d - 90a b c d + 240a b c d + 800a b c )x
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|b \|b x + a
+--R /
+--R 3 +-+
+--R 1280b \|b
+--R Type: Expression(Integer)
+--E 336
+
+--S 337 of 994
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R 5 4 3 4 5 2 3 6 2 2 7 3 8
+--R (150a b d - 900a b c d + 2400a b c d - 4800a b c )x
+--R +
+--R 6 3 3 5 4 2 4 5 2 3 6 3 6
+--R (2400a b d - 14400a b c d + 38400a b c d - 76800a b c )x
+--R +
+--R 7 2 3 6 3 2 5 4 2 4 5 3 4
+--R (10080a b d - 60480a b c d + 161280a b c d - 322560a b c )x
+--R +
+--R 8 3 7 2 2 6 3 2 5 4 3 2
+--R (15360a b d - 92160a b c d + 245760a b c d - 491520a b c )x
+--R +
+--R 9 3 8 2 7 2 2 6 3 3
+--R 7680a d - 46080a b c d + 122880a b c d - 245760a b c
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|a \|b x + a
+--R +
+--R 5 5 3 4 6 2 3 7 2 2 8 3 10
+--R (- 15a b d + 90a b c d - 240a b c d + 480a b c )x
+--R +
+--R 6 4 3 5 5 2 4 6 2 3 7 3 8
+--R (- 750a b d + 4500a b c d - 12000a b c d + 24000a b c )x
+--R +
+--R 7 3 3 6 4 2 5 5 2 4 6 3 6
+--R (- 6000a b d + 36000a b c d - 96000a b c d + 192000a b c )x
+--R +
+--R 8 2 3 7 3 2 6 4 2 5 5 3 4
+--R (- 16800a b d + 100800a b c d - 268800a b c d + 537600a b c )x
+--R +
+--R 9 3 8 2 2 7 3 2 6 4 3 2
+--R (- 19200a b d + 115200a b c d - 307200a b c d + 614400a b c )x
+--R +
+--R 10 3 9 2 8 2 2 7 3 3
+--R - 7680a d + 46080a b c d - 122880a b c d + 245760a b c
+--R *
+--R +--------+
+--R +-+ +-+ | 2 2 +-+ +-+
+--R (\|a \|b + b x)\|b x + a + (- b x - a)\|b - b x\|a
+--R log(--------------------------------------------------------)
+--R +--------+
+--R +-+ | 2
+--R \|a \|b x + a - a
+--R +
+--R 9 3 19 8 3 9 2 17
+--R - 128b d x + (- 6576a b d - 480b c d )x
+--R +
+--R 2 7 3 8 2 9 2 15
+--R (- 60008a b d - 24720a b c d - 640b c d)x
+--R +
+--R 3 6 3 2 7 2 8 2 9 3 13
+--R (- 214150a b d - 228060a b c d - 33120a b c d - 320b c )x
+--R +
+--R 4 5 3 3 6 2 2 7 2 8 3 11
+--R (- 363675a b d - 828510a b c d - 312240a b c d - 16800a b c )x
+--R +
+--R 5 4 3 4 5 2 3 6 2
+--R - 296526a b d - 1440300a b c d - 1176800a b c d
+--R +
+--R 2 7 3
+--R - 168000a b c
+--R *
+--R 9
+--R x
+--R +
+--R 6 3 3 5 4 2 4 5 2 3 6 3 7
+--R (- 95152a b d - 1198560a b c d - 2169600a b c d - 678400a b c )x
+--R +
+--R 7 2 3 6 3 2 5 4 2 4 5 3 5
+--R (- 8096a b d - 344640a b c d - 2030080a b c d - 1305600a b c )x
+--R +
+--R 8 3 7 2 2 6 3 2 5 4 3 3
+--R (- 14080a b d + 84480a b c d - 880640a b c d - 1187840a b c )x
+--R +
+--R 9 3 8 2 7 2 2 6 3 3
+--R (- 7680a d + 46080a b c d - 122880a b c d - 409600a b c )x
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|b \|b x + a
+--R +
+--R 9 3 19 8 3 9 2 17
+--R 1280b d x + (23520a b d + 4800b c d )x
+--R +
+--R 2 7 3 8 2 9 2 15
+--R (136496a b d + 88800a b c d + 6400b c d)x
+--R +
+--R 3 6 3 2 7 2 8 2 9 3 13
+--R (364780a b d + 522360a b c d + 120000a b c d + 3200b c )x
+--R +
+--R 4 5 3 3 6 2 2 7 2 8 3 11
+--R (500210a b d + 1422420a b c d + 725280a b c d + 62400a b c )x
+--R +
+--R 5 4 3 4 5 2 3 6 2 2 7 3 9
+--R (343670a b d + 1993020a b c d + 2058080a b c d + 402240a b c )x
+--R +
+--R 6 3 3 5 4 2 4 5 2 3 6 3 7
+--R (97920a b d + 1378560a b c d + 3082240a b c d + 1208320a b c )x
+--R +
+--R 7 2 3 6 3 2 5 4 2 4 5 3 5
+--R (14176a b d + 308160a b c d + 2455040a b c d + 1848320a b c )x
+--R +
+--R 8 3 7 2 2 6 3 2 5 4 3 3
+--R (17920a b d - 107520a b c d + 942080a b c d + 1392640a b c )x
+--R +
+--R 9 3 8 2 7 2 2 6 3 3
+--R (7680a d - 46080a b c d + 122880a b c d + 409600a b c )x
+--R *
+--R +-+ +-+
+--R \|a \|b
+--R /
+--R 7 8 6 6 2 5 4 3 4 2
+--R 12800b x + 204800a b x + 860160a b x + 1310720a b x
+--R +
+--R 4 3
+--R 655360a b
+--R *
+--R +--------+
+--R +-+ +-+ | 2
+--R \|a \|b \|b x + a
+--R +
+--R 8 10 7 8 2 6 6 3 5 4
+--R - 1280b x - 64000a b x - 512000a b x - 1433600a b x
+--R +
+--R 4 4 2 5 3
+--R - 1638400a b x - 655360a b
+--R *
+--R +-+
+--R \|b
+--R ,
+--R
+--R 5 4 3 4 5 2 3 6 2 2 7 3 8
+--R (- 300a b d + 1800a b c d - 4800a b c d + 9600a b c )x
+--R +
+--R 6 3 3 5 4 2 4 5 2 3 6 3 6
+--R (- 4800a b d + 28800a b c d - 76800a b c d + 153600a b c )x
+--R +
+--R 7 2 3 6 3 2 5 4 2
+--R - 20160a b d + 120960a b c d - 322560a b c d
+--R +
+--R 4 5 3
+--R 645120a b c
+--R *
+--R 4
+--R x
+--R +
+--R 8 3 7 2 2 6 3 2
+--R - 30720a b d + 184320a b c d - 491520a b c d
+--R +
+--R 5 4 3
+--R 983040a b c
+--R *
+--R 2
+--R x
+--R +
+--R 9 3 8 2 7 2 2 6 3 3
+--R - 15360a d + 92160a b c d - 245760a b c d + 491520a b c
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|a \|b x + a
+--R +
+--R 5 5 3 4 6 2 3 7 2 2 8 3 10
+--R (30a b d - 180a b c d + 480a b c d - 960a b c )x
+--R +
+--R 6 4 3 5 5 2 4 6 2 3 7 3 8
+--R (1500a b d - 9000a b c d + 24000a b c d - 48000a b c )x
+--R +
+--R 7 3 3 6 4 2 5 5 2 4 6 3 6
+--R (12000a b d - 72000a b c d + 192000a b c d - 384000a b c )x
+--R +
+--R 8 2 3 7 3 2 6 4 2 5 5 3 4
+--R (33600a b d - 201600a b c d + 537600a b c d - 1075200a b c )x
+--R +
+--R 9 3 8 2 2 7 3 2 6 4 3 2
+--R (38400a b d - 230400a b c d + 614400a b c d - 1228800a b c )x
+--R +
+--R 10 3 9 2 8 2 2 7 3 3
+--R 15360a d - 92160a b c d + 245760a b c d - 491520a b c
+--R *
+--R +--------+
+--R +---+ | 2 +---+ +-+
+--R \|- b \|b x + a - \|- b \|a
+--R atan(------------------------------)
+--R b x
+--R +
+--R 9 3 19 8 3 9 2 17
+--R - 128b d x + (- 6576a b d - 480b c d )x
+--R +
+--R 2 7 3 8 2 9 2 15
+--R (- 60008a b d - 24720a b c d - 640b c d)x
+--R +
+--R 3 6 3 2 7 2 8 2 9 3 13
+--R (- 214150a b d - 228060a b c d - 33120a b c d - 320b c )x
+--R +
+--R 4 5 3 3 6 2 2 7 2 8 3 11
+--R (- 363675a b d - 828510a b c d - 312240a b c d - 16800a b c )x
+--R +
+--R 5 4 3 4 5 2 3 6 2
+--R - 296526a b d - 1440300a b c d - 1176800a b c d
+--R +
+--R 2 7 3
+--R - 168000a b c
+--R *
+--R 9
+--R x
+--R +
+--R 6 3 3 5 4 2 4 5 2 3 6 3 7
+--R (- 95152a b d - 1198560a b c d - 2169600a b c d - 678400a b c )x
+--R +
+--R 7 2 3 6 3 2 5 4 2 4 5 3 5
+--R (- 8096a b d - 344640a b c d - 2030080a b c d - 1305600a b c )x
+--R +
+--R 8 3 7 2 2 6 3 2 5 4 3 3
+--R (- 14080a b d + 84480a b c d - 880640a b c d - 1187840a b c )x
+--R +
+--R 9 3 8 2 7 2 2 6 3 3
+--R (- 7680a d + 46080a b c d - 122880a b c d - 409600a b c )x
+--R *
+--R +--------+
+--R +---+ | 2
+--R \|- b \|b x + a
+--R +
+--R 9 3 19 8 3 9 2 17
+--R 1280b d x + (23520a b d + 4800b c d )x
+--R +
+--R 2 7 3 8 2 9 2 15
+--R (136496a b d + 88800a b c d + 6400b c d)x
+--R +
+--R 3 6 3 2 7 2 8 2 9 3 13
+--R (364780a b d + 522360a b c d + 120000a b c d + 3200b c )x
+--R +
+--R 4 5 3 3 6 2 2 7 2 8 3 11
+--R (500210a b d + 1422420a b c d + 725280a b c d + 62400a b c )x
+--R +
+--R 5 4 3 4 5 2 3 6 2 2 7 3 9
+--R (343670a b d + 1993020a b c d + 2058080a b c d + 402240a b c )x
+--R +
+--R 6 3 3 5 4 2 4 5 2 3 6 3 7
+--R (97920a b d + 1378560a b c d + 3082240a b c d + 1208320a b c )x
+--R +
+--R 7 2 3 6 3 2 5 4 2 4 5 3 5
+--R (14176a b d + 308160a b c d + 2455040a b c d + 1848320a b c )x
+--R +
+--R 8 3 7 2 2 6 3 2 5 4 3 3
+--R (17920a b d - 107520a b c d + 942080a b c d + 1392640a b c )x
+--R +
+--R 9 3 8 2 7 2 2 6 3 3
+--R (7680a d - 46080a b c d + 122880a b c d + 409600a b c )x
+--R *
+--R +---+ +-+
+--R \|- b \|a
+--R /
+--R 7 8 6 6 2 5 4 3 4 2
+--R 12800b x + 204800a b x + 860160a b x + 1310720a b x
+--R +
+--R 4 3
+--R 655360a b
+--R *
+--R +--------+
+--R +---+ +-+ | 2
+--R \|- b \|a \|b x + a
+--R +
+--R 8 10 7 8 2 6 6 3 5 4
+--R - 1280b x - 64000a b x - 512000a b x - 1433600a b x
+--R +
+--R 4 4 2 5 3
+--R - 1638400a b x - 655360a b
+--R *
+--R +---+
+--R \|- b
+--R ]
+--R Type: Union(List(Expression(Integer)),...)
+--E 337
+
+--S 338 of 994
+m0a:=a0.1-r0
+--R
+--R
+--R (4)
+--R 5 3 4 2 3 2 2 2 3 3
+--R (3a d - 18a b c d + 48a b c d - 96a b c )
+--R *
+--R +--------+
+--R +-+ +-+ | 2 2 +-+ +-+
+--R (\|a \|b + b x)\|b x + a + (- b x - a)\|b - b x\|a
+--R log(--------------------------------------------------------)
+--R +--------+
+--R +-+ | 2
+--R \|a \|b x + a - a
+--R +
+--R +-+
+--R 5 3 4 2 3 2 2 2 3 3 x\|b
+--R (3a d - 18a b c d + 48a b c d - 96a b c )atanh(-----------)
+--R +--------+
+--R | 2
+--R \|b x + a
+--R /
+--R 3 +-+
+--R 256b \|b
+--R Type: Expression(Integer)
+--E 338
+
+--S 339 of 994
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 339
+
+--S 340 of 994
+m0b:=a0.2-r0
+--R
+--R
+--R (6)
+--R +-+
+--R 5 3 4 2 3 2 2 2 3 3 +---+ x\|b
+--R (3a d - 18a b c d + 48a b c d - 96a b c )\|- b atanh(-----------)
+--R +--------+
+--R | 2
+--R \|b x + a
+--R +
+--R 5 3 4 2 3 2 2 2 3 3 +-+
+--R (- 6a d + 36a b c d - 96a b c d + 192a b c )\|b
+--R *
+--R +--------+
+--R +---+ | 2 +---+ +-+
+--R \|- b \|b x + a - \|- b \|a
+--R atan(------------------------------)
+--R b x
+--R /
+--R 3 +---+ +-+
+--R 256b \|- b \|b
+--R Type: Expression(Integer)
+--E 340
+
+--S 341 of 994
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 341
+
+)clear all
+
+--S 342 of 994
+t0:=(a+b*x^2)^(3/2)*(c+d*x^2)^2
+--R
+--R
+--R +--------+
+--R 2 6 2 4 2 2 2 | 2
+--R (1) (b d x + (a d + 2b c d)x + (2a c d + b c )x + a c )\|b x + a
+--R Type: Expression(Integer)
+--E 342
+
+--S 343 of 994
+r0:=1/192*(48*b^2*c^2-16*a*b*c*d+3*a^2*d^2)*x*(a+b*x^2)^(3/2)/b^2+_
+ 1/48*d*(10*b*c-3*a*d)*x*(a+b*x^2)^(5/2)/b^2+1/8*d*x*(a+b*_
+ x^2)^(5/2)*(c+d*x^2)/b+1/128*a^2*(48*b^2*c^2-16*a*b*c*d+3*_
+ a^2*d^2)*atanh(x*sqrt(b)/sqrt(a+b*x^2))/b^(5/2)+1/128*a*_
+ (48*b^2*c^2-16*a*b*c*d+3*a^2*d^2)*x*sqrt(a+b*x^2)/b^2
+--R
+--R
+--R (2)
+--R +-+
+--R 4 2 3 2 2 2 x\|b
+--R (9a d - 48a b c d + 144a b c )atanh(-----------)
+--R +--------+
+--R | 2
+--R \|b x + a
+--R +
+--R 3 2 7 2 2 3 5
+--R 48b d x + (72a b d + 128b c d)x
+--R +
+--R 2 2 2 3 2 3 3 2 2 2 2
+--R (6a b d + 224a b c d + 96b c )x + (- 9a d + 48a b c d + 240a b c )x
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|b \|b x + a
+--R /
+--R 2 +-+
+--R 384b \|b
+--R Type: Expression(Integer)
+--E 343
+
+--S 344 of 994
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R 4 3 2 3 4 2 5 2 6
+--R (72a b d - 384a b c d + 1152a b c )x
+--R +
+--R 5 2 2 4 3 3 4 2 4
+--R (720a b d - 3840a b c d + 11520a b c )x
+--R +
+--R 6 2 5 2 4 3 2 2 7 2
+--R (1728a b d - 9216a b c d + 27648a b c )x + 1152a d
+--R +
+--R 6 5 2 2
+--R - 6144a b c d + 18432a b c
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|a \|b x + a
+--R +
+--R 4 4 2 3 5 2 6 2 8
+--R (- 9a b d + 48a b c d - 144a b c )x
+--R +
+--R 5 3 2 4 4 3 5 2 6
+--R (- 288a b d + 1536a b c d - 4608a b c )x
+--R +
+--R 6 2 2 5 3 4 4 2 4
+--R (- 1440a b d + 7680a b c d - 23040a b c )x
+--R +
+--R 7 2 6 2 5 3 2 2 8 2
+--R (- 2304a b d + 12288a b c d - 36864a b c )x - 1152a d
+--R +
+--R 7 6 2 2
+--R 6144a b c d - 18432a b c
+--R *
+--R +--------+
+--R +-+ +-+ | 2 2 +-+ +-+
+--R (\|a \|b - b x)\|b x + a + (- b x - a)\|b + b x\|a
+--R log(--------------------------------------------------------)
+--R +--------+
+--R +-+ | 2
+--R \|a \|b x + a - a
+--R +
+--R 7 2 15 6 2 7 13
+--R - 48b d x + (- 1608a b d - 128b c d)x
+--R +
+--R 2 5 2 6 7 2 11
+--R (- 9990a b d - 4320a b c d - 96b c )x
+--R +
+--R 3 4 2 2 5 6 2 9
+--R (- 23991a b d - 27696a b c d - 3312a b c )x
+--R +
+--R 4 3 2 3 4 2 5 2 7
+--R (- 25248a b d - 70144a b c d - 23040a b c )x
+--R +
+--R 5 2 2 4 3 3 4 2 5
+--R (- 9312a b d - 81408a b c d - 62976a b c )x
+--R +
+--R 6 2 5 2 4 3 2 3
+--R (1536a b d - 40960a b c d - 73728a b c )x
+--R +
+--R 7 2 6 5 2 2
+--R (1152a d - 6144a b c d - 30720a b c )x
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|b \|b x + a
+--R +
+--R 7 2 15 6 2 7 13
+--R 384b d x + (4800a b d + 1024b c d)x
+--R +
+--R 2 5 2 6 7 2 11
+--R (19440a b d + 13056a b c d + 768b c )x
+--R +
+--R 3 4 2 2 5 6 2 9
+--R (35400a b d + 54912a b c d + 10368a b c )x
+--R +
+--R 4 3 2 3 4 2 5 2 7
+--R (30024a b d + 106112a b c d + 47232a b c )x
+--R +
+--R 5 2 2 4 3 3 4 2 5
+--R (8688a b d + 101120a b c d + 96000a b c )x
+--R +
+--R 6 2 5 2 4 3 2 3
+--R (- 2112a b d + 44032a b c d + 89088a b c )x
+--R +
+--R 7 2 6 5 2 2
+--R (- 1152a d + 6144a b c d + 30720a b c )x
+--R *
+--R +-+ +-+
+--R \|a \|b
+--R /
+--R +--------+
+--R 5 6 4 4 2 3 2 3 2 +-+ +-+ | 2
+--R (3072b x + 30720a b x + 73728a b x + 49152a b )\|a \|b \|b x + a
+--R +
+--R 6 8 5 6 2 4 4 3 3 2 4 2 +-+
+--R (- 384b x - 12288a b x - 61440a b x - 98304a b x - 49152a b )\|b
+--R ,
+--R
+--R 4 3 2 3 4 2 5 2 6
+--R (144a b d - 768a b c d + 2304a b c )x
+--R +
+--R 5 2 2 4 3 3 4 2 4
+--R (1440a b d - 7680a b c d + 23040a b c )x
+--R +
+--R 6 2 5 2 4 3 2 2 7 2
+--R (3456a b d - 18432a b c d + 55296a b c )x + 2304a d
+--R +
+--R 6 5 2 2
+--R - 12288a b c d + 36864a b c
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|a \|b x + a
+--R +
+--R 4 4 2 3 5 2 6 2 8
+--R (- 18a b d + 96a b c d - 288a b c )x
+--R +
+--R 5 3 2 4 4 3 5 2 6
+--R (- 576a b d + 3072a b c d - 9216a b c )x
+--R +
+--R 6 2 2 5 3 4 4 2 4
+--R (- 2880a b d + 15360a b c d - 46080a b c )x
+--R +
+--R 7 2 6 2 5 3 2 2 8 2
+--R (- 4608a b d + 24576a b c d - 73728a b c )x - 2304a d
+--R +
+--R 7 6 2 2
+--R 12288a b c d - 36864a b c
+--R *
+--R +--------+
+--R +---+ | 2 +---+ +-+
+--R \|- b \|b x + a - \|- b \|a
+--R atan(------------------------------)
+--R b x
+--R +
+--R 7 2 15 6 2 7 13
+--R - 48b d x + (- 1608a b d - 128b c d)x
+--R +
+--R 2 5 2 6 7 2 11
+--R (- 9990a b d - 4320a b c d - 96b c )x
+--R +
+--R 3 4 2 2 5 6 2 9
+--R (- 23991a b d - 27696a b c d - 3312a b c )x
+--R +
+--R 4 3 2 3 4 2 5 2 7
+--R (- 25248a b d - 70144a b c d - 23040a b c )x
+--R +
+--R 5 2 2 4 3 3 4 2 5
+--R (- 9312a b d - 81408a b c d - 62976a b c )x
+--R +
+--R 6 2 5 2 4 3 2 3
+--R (1536a b d - 40960a b c d - 73728a b c )x
+--R +
+--R 7 2 6 5 2 2
+--R (1152a d - 6144a b c d - 30720a b c )x
+--R *
+--R +--------+
+--R +---+ | 2
+--R \|- b \|b x + a
+--R +
+--R 7 2 15 6 2 7 13
+--R 384b d x + (4800a b d + 1024b c d)x
+--R +
+--R 2 5 2 6 7 2 11
+--R (19440a b d + 13056a b c d + 768b c )x
+--R +
+--R 3 4 2 2 5 6 2 9
+--R (35400a b d + 54912a b c d + 10368a b c )x
+--R +
+--R 4 3 2 3 4 2 5 2 7
+--R (30024a b d + 106112a b c d + 47232a b c )x
+--R +
+--R 5 2 2 4 3 3 4 2 5
+--R (8688a b d + 101120a b c d + 96000a b c )x
+--R +
+--R 6 2 5 2 4 3 2 3
+--R (- 2112a b d + 44032a b c d + 89088a b c )x
+--R +
+--R 7 2 6 5 2 2
+--R (- 1152a d + 6144a b c d + 30720a b c )x
+--R *
+--R +---+ +-+
+--R \|- b \|a
+--R /
+--R +--------+
+--R 5 6 4 4 2 3 2 3 2 +---+ +-+ | 2
+--R (3072b x + 30720a b x + 73728a b x + 49152a b )\|- b \|a \|b x + a
+--R +
+--R 6 8 5 6 2 4 4 3 3 2 4 2 +---+
+--R (- 384b x - 12288a b x - 61440a b x - 98304a b x - 49152a b )\|- b
+--R ]
+--R Type: Union(List(Expression(Integer)),...)
+--E 344
+
+--S 345 of 994
+m0a:=a0.1-r0
+--R
+--R
+--R (4)
+--R 4 2 3 2 2 2
+--R (3a d - 16a b c d + 48a b c )
+--R *
+--R +--------+
+--R +-+ +-+ | 2 2 +-+ +-+
+--R (\|a \|b - b x)\|b x + a + (- b x - a)\|b + b x\|a
+--R log(--------------------------------------------------------)
+--R +--------+
+--R +-+ | 2
+--R \|a \|b x + a - a
+--R +
+--R +-+
+--R 4 2 3 2 2 2 x\|b
+--R (- 3a d + 16a b c d - 48a b c )atanh(-----------)
+--R +--------+
+--R | 2
+--R \|b x + a
+--R /
+--R 2 +-+
+--R 128b \|b
+--R Type: Expression(Integer)
+--E 345
+
+--S 346 of 994
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 346
+
+--S 347 of 994
+m0b:=a0.2-r0
+--R
+--R
+--R (6)
+--R +-+
+--R 4 2 3 2 2 2 +---+ x\|b
+--R (- 3a d + 16a b c d - 48a b c )\|- b atanh(-----------)
+--R +--------+
+--R | 2
+--R \|b x + a
+--R +
+--R +--------+
+--R +---+ | 2 +---+ +-+
+--R 4 2 3 2 2 2 +-+ \|- b \|b x + a - \|- b \|a
+--R (6a d - 32a b c d + 96a b c )\|b atan(------------------------------)
+--R b x
+--R /
+--R 2 +---+ +-+
+--R 128b \|- b \|b
+--R Type: Expression(Integer)
+--E 347
+
+--S 348 of 994
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 348
+
+)clear all
+
+--S 349 of 994
+t0:=(a+b*x^2)^(3/2)*(c+d*x^2)
+--R
+--R
+--R +--------+
+--R 4 2 | 2
+--R (1) (b d x + (a d + b c)x + a c)\|b x + a
+--R Type: Expression(Integer)
+--E 349
+
+--S 350 of 994
+r0:=1/24*(6*b*c-a*d)*x*(a+b*x^2)^(3/2)/b+1/6*d*x*(a+b*x^2)^(5/2)/b+_
+ 1/16*a^2*(6*b*c-a*d)*atanh(x*sqrt(b)/sqrt(a+b*x^2))/b^(3/2)+_
+ 1/16*a*(6*b*c-a*d)*x*sqrt(a+b*x^2)/b
+--R
+--R
+--R (2)
+--R +-+
+--R 3 2 x\|b
+--R (- 3a d + 18a b c)atanh(-----------)
+--R +--------+
+--R | 2
+--R \|b x + a
+--R +
+--R +--------+
+--R 2 5 2 3 2 +-+ | 2
+--R (8b d x + (14a b d + 12b c)x + (3a d + 30a b c)x)\|b \|b x + a
+--R /
+--R +-+
+--R 48b\|b
+--R Type: Expression(Integer)
+--E 350
+
+--S 351 of 994
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R 3 2 2 3 4 4 3 2 2 5
+--R (18a b d - 108a b c)x + (96a b d - 576a b c)x + 96a d
+--R +
+--R 4
+--R - 576a b c
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|a \|b x + a
+--R +
+--R 3 3 2 4 6 4 2 3 3 4
+--R (- 3a b d + 18a b c)x + (- 54a b d + 324a b c)x
+--R +
+--R 5 4 2 2 6 5
+--R (- 144a b d + 864a b c)x - 96a d + 576a b c
+--R *
+--R +--------+
+--R +-+ +-+ | 2 2 +-+ +-+
+--R (\|a \|b + b x)\|b x + a + (- b x - a)\|b - b x\|a
+--R log(--------------------------------------------------------)
+--R +--------+
+--R +-+ | 2
+--R \|a \|b x + a - a
+--R +
+--R 5 11 4 5 9 2 3 4 7
+--R - 8b d x + (- 158a b d - 12b c)x + (- 639a b d - 246a b c)x
+--R +
+--R 3 2 2 3 5 4 3 2 3
+--R (- 982a b d - 1116a b c)x + (- 592a b d - 1824a b c)x
+--R +
+--R 5 4
+--R (- 96a d - 960a b c)x
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|b \|b x + a
+--R +
+--R 5 11 4 5 9 2 3 4 7
+--R 48b d x + (388a b d + 72b c)x + (1062a b d + 636a b c)x
+--R +
+--R 3 2 2 3 5 4 3 2 3
+--R (1266a b d + 1908a b c)x + (640a b d + 2304a b c)x
+--R +
+--R 5 4
+--R (96a d + 960a b c)x
+--R *
+--R +-+ +-+
+--R \|a \|b
+--R /
+--R +--------+
+--R 3 4 2 2 2 +-+ +-+ | 2
+--R (288b x + 1536a b x + 1536a b)\|a \|b \|b x + a
+--R +
+--R 4 6 3 4 2 2 2 3 +-+
+--R (- 48b x - 864a b x - 2304a b x - 1536a b)\|b
+--R ,
+--R
+--R 3 2 2 3 4 4 3 2 2 5
+--R (- 36a b d + 216a b c)x + (- 192a b d + 1152a b c)x - 192a d
+--R +
+--R 4
+--R 1152a b c
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|a \|b x + a
+--R +
+--R 3 3 2 4 6 4 2 3 3 4
+--R (6a b d - 36a b c)x + (108a b d - 648a b c)x
+--R +
+--R 5 4 2 2 6 5
+--R (288a b d - 1728a b c)x + 192a d - 1152a b c
+--R *
+--R +--------+
+--R +---+ | 2 +---+ +-+
+--R \|- b \|b x + a - \|- b \|a
+--R atan(------------------------------)
+--R b x
+--R +
+--R 5 11 4 5 9 2 3 4 7
+--R - 8b d x + (- 158a b d - 12b c)x + (- 639a b d - 246a b c)x
+--R +
+--R 3 2 2 3 5 4 3 2 3
+--R (- 982a b d - 1116a b c)x + (- 592a b d - 1824a b c)x
+--R +
+--R 5 4
+--R (- 96a d - 960a b c)x
+--R *
+--R +--------+
+--R +---+ | 2
+--R \|- b \|b x + a
+--R +
+--R 5 11 4 5 9 2 3 4 7
+--R 48b d x + (388a b d + 72b c)x + (1062a b d + 636a b c)x
+--R +
+--R 3 2 2 3 5 4 3 2 3
+--R (1266a b d + 1908a b c)x + (640a b d + 2304a b c)x
+--R +
+--R 5 4
+--R (96a d + 960a b c)x
+--R *
+--R +---+ +-+
+--R \|- b \|a
+--R /
+--R +--------+
+--R 3 4 2 2 2 +---+ +-+ | 2
+--R (288b x + 1536a b x + 1536a b)\|- b \|a \|b x + a
+--R +
+--R 4 6 3 4 2 2 2 3 +---+
+--R (- 48b x - 864a b x - 2304a b x - 1536a b)\|- b
+--R ]
+--R Type: Union(List(Expression(Integer)),...)
+--E 351
+
+--S 352 of 994
+m0a:=a0.1-r0
+--R
+--R
+--R (4)
+--R 3 2
+--R (a d - 6a b c)
+--R *
+--R +--------+
+--R +-+ +-+ | 2 2 +-+ +-+
+--R (\|a \|b + b x)\|b x + a + (- b x - a)\|b - b x\|a
+--R log(--------------------------------------------------------)
+--R +--------+
+--R +-+ | 2
+--R \|a \|b x + a - a
+--R +
+--R +-+
+--R 3 2 x\|b
+--R (a d - 6a b c)atanh(-----------)
+--R +--------+
+--R | 2
+--R \|b x + a
+--R /
+--R +-+
+--R 16b\|b
+--R Type: Expression(Integer)
+--E 352
+
+--S 353 of 994
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 353
+
+--S 354 of 994
+m0b:=a0.2-r0
+--R
+--R
+--R (6)
+--R +-+
+--R 3 2 +---+ x\|b
+--R (a d - 6a b c)\|- b atanh(-----------)
+--R +--------+
+--R | 2
+--R \|b x + a
+--R +
+--R +--------+
+--R +---+ | 2 +---+ +-+
+--R 3 2 +-+ \|- b \|b x + a - \|- b \|a
+--R (- 2a d + 12a b c)\|b atan(------------------------------)
+--R b x
+--R /
+--R +---+ +-+
+--R 16b\|- b \|b
+--R Type: Expression(Integer)
+--E 354
+
+--S 355 of 994
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 355
+
+)clear all
+
+--S 356 of 994
+t0:=(a+b*x^2)^(3/2)
+--R
+--R
+--R +--------+
+--R 2 | 2
+--R (1) (b x + a)\|b x + a
+--R Type: Expression(Integer)
+--E 356
+
+--S 357 of 994
+r0:=1/4*x*(a+b*x^2)^(3/2)+3/8*a^2*atanh(x*sqrt(b)/sqrt(a+b*x^2))/_
+ sqrt(b)+3/8*a*x*sqrt(a+b*x^2)
+--R
+--R
+--R +-+ +--------+
+--R 2 x\|b 3 +-+ | 2
+--R 3a atanh(-----------) + (2b x + 5a x)\|b \|b x + a
+--R +--------+
+--R | 2
+--R \|b x + a
+--R (2) -----------------------------------------------------
+--R +-+
+--R 8\|b
+--R Type: Expression(Integer)
+--E 357
+
+--S 358 of 994
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R +--------+
+--R 2 2 3 +-+ | 2 2 2 4 3 2 4
+--R ((12a b x + 24a )\|a \|b x + a - 3a b x - 24a b x - 24a )
+--R *
+--R +--------+
+--R +-+ +-+ | 2 2 +-+ +-+
+--R (\|a \|b - b x)\|b x + a + (- b x - a)\|b + b x\|a
+--R log(--------------------------------------------------------)
+--R +--------+
+--R +-+ | 2
+--R \|a \|b x + a - a
+--R +
+--R +--------+
+--R 3 7 2 5 2 3 3 +-+ | 2
+--R (- 2b x - 21a b x - 56a b x - 40a x)\|b \|b x + a
+--R +
+--R 3 7 2 5 2 3 3 +-+ +-+
+--R (8b x + 44a b x + 76a b x + 40a x)\|a \|b
+--R /
+--R +--------+
+--R 2 +-+ +-+ | 2 2 4 2 2 +-+
+--R (32b x + 64a)\|a \|b \|b x + a + (- 8b x - 64a b x - 64a )\|b
+--R ,
+--R
+--R +--------+
+--R 2 2 3 +-+ | 2 2 2 4 3 2 4
+--R ((24a b x + 48a )\|a \|b x + a - 6a b x - 48a b x - 48a )
+--R *
+--R +--------+
+--R +---+ | 2 +---+ +-+
+--R \|- b \|b x + a - \|- b \|a
+--R atan(------------------------------)
+--R b x
+--R +
+--R +--------+
+--R 3 7 2 5 2 3 3 +---+ | 2
+--R (- 2b x - 21a b x - 56a b x - 40a x)\|- b \|b x + a
+--R +
+--R 3 7 2 5 2 3 3 +---+ +-+
+--R (8b x + 44a b x + 76a b x + 40a x)\|- b \|a
+--R /
+--R +--------+
+--R 2 +---+ +-+ | 2 2 4 2 2 +---+
+--R (32b x + 64a)\|- b \|a \|b x + a + (- 8b x - 64a b x - 64a )\|- b
+--R ]
+--R Type: Union(List(Expression(Integer)),...)
+--E 358
+
+--S 359 of 994
+m0a:=a0.1-r0
+--R
+--R
+--R (4)
+--R +--------+
+--R +-+ +-+ | 2 2 +-+ +-+
+--R 2 (\|a \|b - b x)\|b x + a + (- b x - a)\|b + b x\|a
+--R 3a log(--------------------------------------------------------)
+--R +--------+
+--R +-+ | 2
+--R \|a \|b x + a - a
+--R +
+--R +-+
+--R 2 x\|b
+--R - 3a atanh(-----------)
+--R +--------+
+--R | 2
+--R \|b x + a
+--R /
+--R +-+
+--R 8\|b
+--R Type: Expression(Integer)
+--E 359
+
+--S 360 of 994
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 360
+
+--S 361 of 994
+m0b:=a0.2-r0
+--R
+--R
+--R (6)
+--R +--------+
+--R +-+ +---+ | 2 +---+ +-+
+--R 2 +---+ x\|b 2 +-+ \|- b \|b x + a - \|- b \|a
+--R - 3a \|- b atanh(-----------) + 6a \|b atan(------------------------------)
+--R +--------+ b x
+--R | 2
+--R \|b x + a
+--R ---------------------------------------------------------------------------
+--R +---+ +-+
+--R 8\|- b \|b
+--R Type: Expression(Integer)
+--E 361
+
+--S 362 of 994
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 362
+
+)clear all
+
+--S 363 of 994
+t0:=(a+b*x^2)^(3/2)/(c+d*x^2)
+--R
+--R
+--R +--------+
+--R 2 | 2
+--R (b x + a)\|b x + a
+--R (1) ---------------------
+--R 2
+--R d x + c
+--R Type: Expression(Integer)
+--E 363
+
+--S 364 of 994
+r0:=-1/2*(2*b*c-3*a*d)*atanh(x*sqrt(b)/sqrt(a+b*x^2))*sqrt(b)/d^2+_
+ (b*c-a*d)^(3/2)*atanh(x*sqrt(b*c-a*d)/(sqrt(c)*sqrt(a+b*x^2)))/_
+ (d^2*sqrt(c))+1/2*b*x*sqrt(a+b*x^2)/d
+--R
+--R
+--R (2)
+--R +-+
+--R +-+ +-+ x\|b
+--R (3a d - 2b c)\|b \|c atanh(-----------)
+--R +--------+
+--R | 2
+--R \|b x + a
+--R +
+--R +-----------+ +--------+
+--R +-----------+ x\|- a d + b c +-+ | 2
+--R (- 2a d + 2b c)\|- a d + b c atanh(---------------) + b d x\|c \|b x + a
+--R +--------+
+--R +-+ | 2
+--R \|c \|b x + a
+--R /
+--R 2 +-+
+--R 2d \|c
+--R Type: Expression(Integer)
+--E 364
+
+--S 365 of 994
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R +-----------+ +--------+
+--R |- a d + b c +-+ | 2
+--R (2a d - 2b c) |----------- \|a \|b x + a
+--R \| c
+--R +
+--R +-----------+
+--R 2 2 2 |- a d + b c
+--R ((- a b d + b c)x - 2a d + 2a b c) |-----------
+--R \| c
+--R *
+--R log
+--R 2 +-+
+--R ((- 2a d + 4b c)x + 2a c)\|a
+--R +
+--R +-----------+
+--R 3 |- a d + b c
+--R (2b c x + 4a c x) |-----------
+--R \| c
+--R *
+--R +--------+
+--R | 2
+--R \|b x + a
+--R +
+--R +-----------+
+--R 3 |- a d + b c +-+ 2 4
+--R (- 4b c x - 4a c x) |----------- \|a + (a b d - 2b c)x
+--R \| c
+--R +
+--R 2 2 2
+--R (2a d - 5a b c)x - 2a c
+--R /
+--R +--------+
+--R 2 +-+ | 2 4 2
+--R (2d x + 2c)\|a \|b x + a - b d x + (- 2a d - b c)x - 2a c
+--R +
+--R +--------+
+--R +-+ +-+ | 2
+--R (6a d - 4b c)\|a \|b \|b x + a
+--R +
+--R 2 2 2 +-+
+--R ((- 3a b d + 2b c)x - 6a d + 4a b c)\|b
+--R *
+--R +--------+
+--R +-+ +-+ | 2 +-+ +-+ 2
+--R (- x\|b + \|a )\|b x + a + x\|a \|b - b x - a
+--R log(--------------------------------------------------)
+--R +--------+
+--R +-+ | 2
+--R \|a \|b x + a - a
+--R +
+--R +--------+
+--R 2 3 | 2 2 3 +-+
+--R (- b d x - 2a b d x)\|b x + a + (2b d x + 2a b d x)\|a
+--R /
+--R +--------+
+--R 2 +-+ | 2 2 2 2
+--R 4d \|a \|b x + a - 2b d x - 4a d
+--R ,
+--R
+--R +--------+
+--R +-+ +-+ | 2
+--R (6a d - 4b c)\|a \|b \|b x + a
+--R +
+--R 2 2 2 +-+
+--R ((- 3a b d + 2b c)x - 6a d + 4a b c)\|b
+--R *
+--R +--------+
+--R +-+ +-+ | 2 +-+ +-+ 2
+--R (- x\|b + \|a )\|b x + a + x\|a \|b - b x - a
+--R log(--------------------------------------------------)
+--R +--------+
+--R +-+ | 2
+--R \|a \|b x + a - a
+--R +
+--R +---------+ +--------+
+--R +-+ |a d - b c | 2
+--R (4a d - 4b c)\|a |--------- \|b x + a
+--R \| c
+--R +
+--R +---------+
+--R 2 2 2 |a d - b c
+--R ((- 2a b d + 2b c)x - 4a d + 4a b c) |---------
+--R \| c
+--R *
+--R +--------+
+--R 2 | 2 2 +-+
+--R ((a d - b c)x + a c)\|b x + a + (- a d x - a c)\|a
+--R atan(-------------------------------------------------------)
+--R +---------+
+--R 3 |a d - b c
+--R b c x |---------
+--R \| c
+--R +
+--R +---------+ +--------+
+--R +-+ |a d - b c | 2
+--R (4a d - 4b c)\|a |--------- \|b x + a
+--R \| c
+--R +
+--R +---------+
+--R 2 2 2 |a d - b c
+--R ((- 2a b d + 2b c)x - 4a d + 4a b c) |---------
+--R \| c
+--R *
+--R +-+
+--R \|a
+--R atan(-------------)
+--R +---------+
+--R |a d - b c
+--R x |---------
+--R \| c
+--R +
+--R +--------+
+--R 2 3 | 2 2 3 +-+
+--R (- b d x - 2a b d x)\|b x + a + (2b d x + 2a b d x)\|a
+--R /
+--R +--------+
+--R 2 +-+ | 2 2 2 2
+--R 4d \|a \|b x + a - 2b d x - 4a d
+--R ,
+--R
+--R +-----------+ +--------+
+--R |- a d + b c +-+ | 2
+--R (2a d - 2b c) |----------- \|a \|b x + a
+--R \| c
+--R +
+--R +-----------+
+--R 2 2 2 |- a d + b c
+--R ((- a b d + b c)x - 2a d + 2a b c) |-----------
+--R \| c
+--R *
+--R log
+--R 2 +-+
+--R ((- 2a d + 4b c)x + 2a c)\|a
+--R +
+--R +-----------+
+--R 3 |- a d + b c
+--R (2b c x + 4a c x) |-----------
+--R \| c
+--R *
+--R +--------+
+--R | 2
+--R \|b x + a
+--R +
+--R +-----------+
+--R 3 |- a d + b c +-+ 2 4
+--R (- 4b c x - 4a c x) |----------- \|a + (a b d - 2b c)x
+--R \| c
+--R +
+--R 2 2 2
+--R (2a d - 5a b c)x - 2a c
+--R /
+--R +--------+
+--R 2 +-+ | 2 4 2
+--R (2d x + 2c)\|a \|b x + a - b d x + (- 2a d - b c)x - 2a c
+--R +
+--R +--------+
+--R +---+ +-+ | 2
+--R (12a d - 8b c)\|- b \|a \|b x + a
+--R +
+--R 2 2 2 +---+
+--R ((- 6a b d + 4b c)x - 12a d + 8a b c)\|- b
+--R *
+--R +--------+
+--R | 2 +-+
+--R \|b x + a - \|a
+--R atan(------------------)
+--R +---+
+--R x\|- b
+--R +
+--R +--------+
+--R 2 3 | 2 2 3 +-+
+--R (- b d x - 2a b d x)\|b x + a + (2b d x + 2a b d x)\|a
+--R /
+--R +--------+
+--R 2 +-+ | 2 2 2 2
+--R 4d \|a \|b x + a - 2b d x - 4a d
+--R ,
+--R
+--R +--------+
+--R +---+ +-+ | 2
+--R (12a d - 8b c)\|- b \|a \|b x + a
+--R +
+--R 2 2 2 +---+
+--R ((- 6a b d + 4b c)x - 12a d + 8a b c)\|- b
+--R *
+--R +--------+
+--R | 2 +-+
+--R \|b x + a - \|a
+--R atan(------------------)
+--R +---+
+--R x\|- b
+--R +
+--R +---------+ +--------+
+--R +-+ |a d - b c | 2
+--R (4a d - 4b c)\|a |--------- \|b x + a
+--R \| c
+--R +
+--R +---------+
+--R 2 2 2 |a d - b c
+--R ((- 2a b d + 2b c)x - 4a d + 4a b c) |---------
+--R \| c
+--R *
+--R +--------+
+--R 2 | 2 2 +-+
+--R ((a d - b c)x + a c)\|b x + a + (- a d x - a c)\|a
+--R atan(-------------------------------------------------------)
+--R +---------+
+--R 3 |a d - b c
+--R b c x |---------
+--R \| c
+--R +
+--R +---------+ +--------+
+--R +-+ |a d - b c | 2
+--R (4a d - 4b c)\|a |--------- \|b x + a
+--R \| c
+--R +
+--R +---------+
+--R 2 2 2 |a d - b c
+--R ((- 2a b d + 2b c)x - 4a d + 4a b c) |---------
+--R \| c
+--R *
+--R +-+
+--R \|a
+--R atan(-------------)
+--R +---------+
+--R |a d - b c
+--R x |---------
+--R \| c
+--R +
+--R +--------+
+--R 2 3 | 2 2 3 +-+
+--R (- b d x - 2a b d x)\|b x + a + (2b d x + 2a b d x)\|a
+--R /
+--R +--------+
+--R 2 +-+ | 2 2 2 2
+--R 4d \|a \|b x + a - 2b d x - 4a d
+--R ]
+--R Type: Union(List(Expression(Integer)),...)
+--E 365
+
+--S 366 of 994
+m0a:=a0.1-r0
+--R
+--R
+--R (4)
+--R +-----------+
+--R |- a d + b c +-+
+--R (a d - b c) |----------- \|c
+--R \| c
+--R *
+--R log
+--R 2 +-+
+--R ((- 2a d + 4b c)x + 2a c)\|a
+--R +
+--R +-----------+
+--R 3 |- a d + b c
+--R (2b c x + 4a c x) |-----------
+--R \| c
+--R *
+--R +--------+
+--R | 2
+--R \|b x + a
+--R +
+--R +-----------+
+--R 3 |- a d + b c +-+ 2 4
+--R (- 4b c x - 4a c x) |----------- \|a + (a b d - 2b c)x
+--R \| c
+--R +
+--R 2 2 2
+--R (2a d - 5a b c)x - 2a c
+--R /
+--R +--------+
+--R 2 +-+ | 2 4 2
+--R (2d x + 2c)\|a \|b x + a - b d x + (- 2a d - b c)x - 2a c
+--R +
+--R +-+ +-+
+--R (3a d - 2b c)\|b \|c
+--R *
+--R +--------+
+--R +-+ +-+ | 2 +-+ +-+ 2
+--R (- x\|b + \|a )\|b x + a + x\|a \|b - b x - a
+--R log(--------------------------------------------------)
+--R +--------+
+--R +-+ | 2
+--R \|a \|b x + a - a
+--R +
+--R +-+
+--R +-+ +-+ x\|b
+--R (- 3a d + 2b c)\|b \|c atanh(-----------)
+--R +--------+
+--R | 2
+--R \|b x + a
+--R +
+--R +-----------+
+--R +-----------+ x\|- a d + b c
+--R (2a d - 2b c)\|- a d + b c atanh(---------------)
+--R +--------+
+--R +-+ | 2
+--R \|c \|b x + a
+--R /
+--R 2 +-+
+--R 2d \|c
+--R Type: Expression(Integer)
+--E 366
+
+--S 367 of 994
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 367
+
+--S 368 of 994
+m0b:=a0.2-r0
+--R
+--R
+--R (6)
+--R +-+ +-+
+--R (3a d - 2b c)\|b \|c
+--R *
+--R +--------+
+--R +-+ +-+ | 2 +-+ +-+ 2
+--R (- x\|b + \|a )\|b x + a + x\|a \|b - b x - a
+--R log(--------------------------------------------------)
+--R +--------+
+--R +-+ | 2
+--R \|a \|b x + a - a
+--R +
+--R +-+
+--R +-+ +-+ x\|b
+--R (- 3a d + 2b c)\|b \|c atanh(-----------)
+--R +--------+
+--R | 2
+--R \|b x + a
+--R +
+--R +-----------+
+--R +-----------+ x\|- a d + b c
+--R (2a d - 2b c)\|- a d + b c atanh(---------------)
+--R +--------+
+--R +-+ | 2
+--R \|c \|b x + a
+--R +
+--R +---------+
+--R +-+ |a d - b c
+--R (2a d - 2b c)\|c |---------
+--R \| c
+--R *
+--R +--------+
+--R 2 | 2 2 +-+
+--R ((a d - b c)x + a c)\|b x + a + (- a d x - a c)\|a
+--R atan(-------------------------------------------------------)
+--R +---------+
+--R 3 |a d - b c
+--R b c x |---------
+--R \| c
+--R +
+--R +---------+ +-+
+--R +-+ |a d - b c \|a
+--R (2a d - 2b c)\|c |--------- atan(-------------)
+--R \| c +---------+
+--R |a d - b c
+--R x |---------
+--R \| c
+--R /
+--R 2 +-+
+--R 2d \|c
+--R Type: Expression(Integer)
+--E 368
+
+--S 369 of 994
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 369
+
+)clear all
+
+--S 370 of 994
+t0:=(a+b*x^2)^(3/2)/(c+d*x^2)^2
+--R
+--R
+--R +--------+
+--R 2 | 2
+--R (b x + a)\|b x + a
+--R (1) ---------------------
+--R 2 4 2 2
+--R d x + 2c d x + c
+--R Type: Expression(Integer)
+--E 370
+
+--S 371 of 994
+r0:=b^(3/2)*atanh(x*sqrt(b)/sqrt(a+b*x^2))/d^2-1/2*(2*b*c+a*d)*_
+ atanh(x*sqrt(b*c-a*d)/(sqrt(c)*sqrt(a+b*x^2)))*sqrt(b*c-a*d)/_
+ (c^(3/2)*d^2)-1/2*(b*c-a*d)*x*sqrt(a+b*x^2)/(c*d*(c+d*x^2))
+--R
+--R
+--R (2)
+--R +-+
+--R 2 2 +-+ +-+ x\|b
+--R (2b c d x + 2b c )\|b \|c atanh(-----------)
+--R +--------+
+--R | 2
+--R \|b x + a
+--R +
+--R +-----------+
+--R 2 2 2 +-----------+ x\|- a d + b c
+--R ((- a d - 2b c d)x - a c d - 2b c )\|- a d + b c atanh(---------------)
+--R +--------+
+--R +-+ | 2
+--R \|c \|b x + a
+--R +
+--R +--------+
+--R 2 +-+ | 2
+--R (a d - b c d)x\|c \|b x + a
+--R /
+--R 3 2 2 2 +-+
+--R (2c d x + 2c d )\|c
+--R Type: Expression(Integer)
+--E 371
+
+--S 372 of 994
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R +-----------+ +--------+
+--R 2 2 2 |- a d + b c +-+ | 2
+--R ((2a d + 4b c d)x + 2a c d + 4b c ) |----------- \|a \|b x + a
+--R \| c
+--R +
+--R 2 2 4 2 2 2 2 2 2
+--R (- a b d - 2b c d)x + (- 2a d - 5a b c d - 2b c )x - 2a c d
+--R +
+--R 2
+--R - 4a b c
+--R *
+--R +-----------+
+--R |- a d + b c
+--R |-----------
+--R \| c
+--R *
+--R log
+--R 2 +-+
+--R ((- 2a d + 4b c)x + 2a c)\|a
+--R +
+--R +-----------+
+--R 3 |- a d + b c
+--R (2b c x + 4a c x) |-----------
+--R \| c
+--R *
+--R +--------+
+--R | 2
+--R \|b x + a
+--R +
+--R +-----------+
+--R 3 |- a d + b c +-+ 2 4
+--R (- 4b c x - 4a c x) |----------- \|a + (a b d - 2b c)x
+--R \| c
+--R +
+--R 2 2 2
+--R (2a d - 5a b c)x - 2a c
+--R /
+--R +--------+
+--R 2 +-+ | 2 4 2
+--R (2d x + 2c)\|a \|b x + a - b d x + (- 2a d - b c)x - 2a c
+--R +
+--R +--------+
+--R 2 2 +-+ +-+ | 2
+--R (8b c d x + 8b c )\|a \|b \|b x + a
+--R +
+--R 2 4 2 2 2 2 +-+
+--R (- 4b c d x + (- 8a b c d - 4b c )x - 8a b c )\|b
+--R *
+--R +--------+
+--R +-+ +-+ | 2 +-+ +-+ 2
+--R (- x\|b + \|a )\|b x + a + x\|a \|b - b x - a
+--R log(--------------------------------------------------)
+--R +--------+
+--R +-+ | 2
+--R \|a \|b x + a - a
+--R +
+--R +--------+
+--R 2 2 3 2 2 | 2
+--R ((- 2a b d + 2b c d)x + (- 4a d + 4a b c d)x)\|b x + a
+--R +
+--R 2 2 3 2 2 +-+
+--R ((4a b d - 4b c d)x + (4a d - 4a b c d)x)\|a
+--R /
+--R +--------+
+--R 3 2 2 2 +-+ | 2 3 4 3 2 2 2
+--R (8c d x + 8c d )\|a \|b x + a - 4b c d x + (- 8a c d - 4b c d )x
+--R +
+--R 2 2
+--R - 8a c d
+--R ,
+--R
+--R +--------+
+--R 2 2 +-+ +-+ | 2
+--R (4b c d x + 4b c )\|a \|b \|b x + a
+--R +
+--R 2 4 2 2 2 2 +-+
+--R (- 2b c d x + (- 4a b c d - 2b c )x - 4a b c )\|b
+--R *
+--R +--------+
+--R +-+ +-+ | 2 +-+ +-+ 2
+--R (- x\|b + \|a )\|b x + a + x\|a \|b - b x - a
+--R log(--------------------------------------------------)
+--R +--------+
+--R +-+ | 2
+--R \|a \|b x + a - a
+--R +
+--R +---------+ +--------+
+--R 2 2 2 +-+ |a d - b c | 2
+--R ((2a d + 4b c d)x + 2a c d + 4b c )\|a |--------- \|b x + a
+--R \| c
+--R +
+--R 2 2 4 2 2 2 2 2 2
+--R (- a b d - 2b c d)x + (- 2a d - 5a b c d - 2b c )x - 2a c d
+--R +
+--R 2
+--R - 4a b c
+--R *
+--R +---------+
+--R |a d - b c
+--R |---------
+--R \| c
+--R *
+--R +--------+
+--R 2 | 2 2 +-+
+--R ((a d - b c)x + a c)\|b x + a + (- a d x - a c)\|a
+--R atan(-------------------------------------------------------)
+--R +---------+
+--R 3 |a d - b c
+--R b c x |---------
+--R \| c
+--R +
+--R +---------+ +--------+
+--R 2 2 2 +-+ |a d - b c | 2
+--R ((2a d + 4b c d)x + 2a c d + 4b c )\|a |--------- \|b x + a
+--R \| c
+--R +
+--R 2 2 4 2 2 2 2 2 2
+--R (- a b d - 2b c d)x + (- 2a d - 5a b c d - 2b c )x - 2a c d
+--R +
+--R 2
+--R - 4a b c
+--R *
+--R +---------+
+--R |a d - b c
+--R |---------
+--R \| c
+--R *
+--R +-+
+--R \|a
+--R atan(-------------)
+--R +---------+
+--R |a d - b c
+--R x |---------
+--R \| c
+--R +
+--R +--------+
+--R 2 2 3 2 2 | 2
+--R ((- a b d + b c d)x + (- 2a d + 2a b c d)x)\|b x + a
+--R +
+--R 2 2 3 2 2 +-+
+--R ((2a b d - 2b c d)x + (2a d - 2a b c d)x)\|a
+--R /
+--R +--------+
+--R 3 2 2 2 +-+ | 2 3 4 3 2 2 2
+--R (4c d x + 4c d )\|a \|b x + a - 2b c d x + (- 4a c d - 2b c d )x
+--R +
+--R 2 2
+--R - 4a c d
+--R ,
+--R
+--R +-----------+ +--------+
+--R 2 2 2 |- a d + b c +-+ | 2
+--R ((2a d + 4b c d)x + 2a c d + 4b c ) |----------- \|a \|b x + a
+--R \| c
+--R +
+--R 2 2 4 2 2 2 2 2 2
+--R (- a b d - 2b c d)x + (- 2a d - 5a b c d - 2b c )x - 2a c d
+--R +
+--R 2
+--R - 4a b c
+--R *
+--R +-----------+
+--R |- a d + b c
+--R |-----------
+--R \| c
+--R *
+--R log
+--R 2 +-+
+--R ((- 2a d + 4b c)x + 2a c)\|a
+--R +
+--R +-----------+
+--R 3 |- a d + b c
+--R (2b c x + 4a c x) |-----------
+--R \| c
+--R *
+--R +--------+
+--R | 2
+--R \|b x + a
+--R +
+--R +-----------+
+--R 3 |- a d + b c +-+ 2 4
+--R (- 4b c x - 4a c x) |----------- \|a + (a b d - 2b c)x
+--R \| c
+--R +
+--R 2 2 2
+--R (2a d - 5a b c)x - 2a c
+--R /
+--R +--------+
+--R 2 +-+ | 2 4 2
+--R (2d x + 2c)\|a \|b x + a - b d x + (- 2a d - b c)x - 2a c
+--R +
+--R +--------+
+--R 2 2 +---+ +-+ | 2
+--R (16b c d x + 16b c )\|- b \|a \|b x + a
+--R +
+--R 2 4 2 2 2 2 +---+
+--R (- 8b c d x + (- 16a b c d - 8b c )x - 16a b c )\|- b
+--R *
+--R +--------+
+--R | 2 +-+
+--R \|b x + a - \|a
+--R atan(------------------)
+--R +---+
+--R x\|- b
+--R +
+--R +--------+
+--R 2 2 3 2 2 | 2
+--R ((- 2a b d + 2b c d)x + (- 4a d + 4a b c d)x)\|b x + a
+--R +
+--R 2 2 3 2 2 +-+
+--R ((4a b d - 4b c d)x + (4a d - 4a b c d)x)\|a
+--R /
+--R +--------+
+--R 3 2 2 2 +-+ | 2 3 4 3 2 2 2
+--R (8c d x + 8c d )\|a \|b x + a - 4b c d x + (- 8a c d - 4b c d )x
+--R +
+--R 2 2
+--R - 8a c d
+--R ,
+--R
+--R +--------+
+--R 2 2 +---+ +-+ | 2
+--R (8b c d x + 8b c )\|- b \|a \|b x + a
+--R +
+--R 2 4 2 2 2 2 +---+
+--R (- 4b c d x + (- 8a b c d - 4b c )x - 8a b c )\|- b
+--R *
+--R +--------+
+--R | 2 +-+
+--R \|b x + a - \|a
+--R atan(------------------)
+--R +---+
+--R x\|- b
+--R +
+--R +---------+ +--------+
+--R 2 2 2 +-+ |a d - b c | 2
+--R ((2a d + 4b c d)x + 2a c d + 4b c )\|a |--------- \|b x + a
+--R \| c
+--R +
+--R 2 2 4 2 2 2 2 2 2
+--R (- a b d - 2b c d)x + (- 2a d - 5a b c d - 2b c )x - 2a c d
+--R +
+--R 2
+--R - 4a b c
+--R *
+--R +---------+
+--R |a d - b c
+--R |---------
+--R \| c
+--R *
+--R +--------+
+--R 2 | 2 2 +-+
+--R ((a d - b c)x + a c)\|b x + a + (- a d x - a c)\|a
+--R atan(-------------------------------------------------------)
+--R +---------+
+--R 3 |a d - b c
+--R b c x |---------
+--R \| c
+--R +
+--R +---------+ +--------+
+--R 2 2 2 +-+ |a d - b c | 2
+--R ((2a d + 4b c d)x + 2a c d + 4b c )\|a |--------- \|b x + a
+--R \| c
+--R +
+--R 2 2 4 2 2 2 2 2 2
+--R (- a b d - 2b c d)x + (- 2a d - 5a b c d - 2b c )x - 2a c d
+--R +
+--R 2
+--R - 4a b c
+--R *
+--R +---------+
+--R |a d - b c
+--R |---------
+--R \| c
+--R *
+--R +-+
+--R \|a
+--R atan(-------------)
+--R +---------+
+--R |a d - b c
+--R x |---------
+--R \| c
+--R +
+--R +--------+
+--R 2 2 3 2 2 | 2
+--R ((- a b d + b c d)x + (- 2a d + 2a b c d)x)\|b x + a
+--R +
+--R 2 2 3 2 2 +-+
+--R ((2a b d - 2b c d)x + (2a d - 2a b c d)x)\|a
+--R /
+--R +--------+
+--R 3 2 2 2 +-+ | 2 3 4 3 2 2 2
+--R (4c d x + 4c d )\|a \|b x + a - 2b c d x + (- 4a c d - 2b c d )x
+--R +
+--R 2 2
+--R - 4a c d
+--R ]
+--R Type: Union(List(Expression(Integer)),...)
+--E 372
+
+--S 373 of 994
+m0a:=a0.1-r0
+--R
+--R
+--R (4)
+--R +-----------+
+--R |- a d + b c +-+
+--R (a d + 2b c) |----------- \|c
+--R \| c
+--R *
+--R log
+--R 2 +-+
+--R ((- 2a d + 4b c)x + 2a c)\|a
+--R +
+--R +-----------+
+--R 3 |- a d + b c
+--R (2b c x + 4a c x) |-----------
+--R \| c
+--R *
+--R +--------+
+--R | 2
+--R \|b x + a
+--R +
+--R +-----------+
+--R 3 |- a d + b c +-+ 2 4
+--R (- 4b c x - 4a c x) |----------- \|a + (a b d - 2b c)x
+--R \| c
+--R +
+--R 2 2 2
+--R (2a d - 5a b c)x - 2a c
+--R /
+--R +--------+
+--R 2 +-+ | 2 4 2
+--R (2d x + 2c)\|a \|b x + a - b d x + (- 2a d - b c)x - 2a c
+--R +
+--R +--------+
+--R +-+ +-+ | 2 +-+ +-+ 2
+--R +-+ +-+ (- x\|b + \|a )\|b x + a + x\|a \|b - b x - a
+--R 4b c\|b \|c log(--------------------------------------------------)
+--R +--------+
+--R +-+ | 2
+--R \|a \|b x + a - a
+--R +
+--R +-+
+--R +-+ +-+ x\|b
+--R - 4b c\|b \|c atanh(-----------)
+--R +--------+
+--R | 2
+--R \|b x + a
+--R +
+--R +-----------+
+--R +-----------+ x\|- a d + b c
+--R (2a d + 4b c)\|- a d + b c atanh(---------------)
+--R +--------+
+--R +-+ | 2
+--R \|c \|b x + a
+--R /
+--R 2 +-+
+--R 4c d \|c
+--R Type: Expression(Integer)
+--E 373
+
+--S 374 of 994
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 374
+
+--S 375 of 994
+m0b:=a0.2-r0
+--R
+--R
+--R (6)
+--R +--------+
+--R +-+ +-+ | 2 +-+ +-+ 2
+--R +-+ +-+ (- x\|b + \|a )\|b x + a + x\|a \|b - b x - a
+--R 2b c\|b \|c log(--------------------------------------------------)
+--R +--------+
+--R +-+ | 2
+--R \|a \|b x + a - a
+--R +
+--R +-+
+--R +-+ +-+ x\|b
+--R - 2b c\|b \|c atanh(-----------)
+--R +--------+
+--R | 2
+--R \|b x + a
+--R +
+--R +-----------+
+--R +-----------+ x\|- a d + b c
+--R (a d + 2b c)\|- a d + b c atanh(---------------)
+--R +--------+
+--R +-+ | 2
+--R \|c \|b x + a
+--R +
+--R +---------+
+--R +-+ |a d - b c
+--R (a d + 2b c)\|c |---------
+--R \| c
+--R *
+--R +--------+
+--R 2 | 2 2 +-+
+--R ((a d - b c)x + a c)\|b x + a + (- a d x - a c)\|a
+--R atan(-------------------------------------------------------)
+--R +---------+
+--R 3 |a d - b c
+--R b c x |---------
+--R \| c
+--R +
+--R +---------+ +-+
+--R +-+ |a d - b c \|a
+--R (a d + 2b c)\|c |--------- atan(-------------)
+--R \| c +---------+
+--R |a d - b c
+--R x |---------
+--R \| c
+--R /
+--R 2 +-+
+--R 2c d \|c
+--R Type: Expression(Integer)
+--E 375
+
+--S 376 of 994
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 376
+
+)clear all
+
+--S 377 of 994
+t0:=(a+b*x^2)^(3/2)/(c+d*x^2)^3
+--R
+--R
+--R +--------+
+--R 2 | 2
+--R (b x + a)\|b x + a
+--R (1) -----------------------------
+--R 3 6 2 4 2 2 3
+--R d x + 3c d x + 3c d x + c
+--R Type: Expression(Integer)
+--E 377
+
+--S 378 of 994
+r0:=3/8*a^2*atanh(x*sqrt(b*c-a*d)/(sqrt(c)*sqrt(a+b*x^2)))/(c^(5/2)*_
+ sqrt(b*c-a*d))-1/4*(b*c-a*d)*x*sqrt(a+b*x^2)/(c*d*(c+d*x^2)^2)+_
+ 1/8*(2*b*c+3*a*d)*x*sqrt(a+b*x^2)/(c^2*d*(c+d*x^2))
+--R
+--R
+--R (2)
+--R +-----------+
+--R 2 2 4 2 2 2 2 x\|- a d + b c
+--R (3a d x + 6a c d x + 3a c )atanh(---------------)
+--R +--------+
+--R +-+ | 2
+--R \|c \|b x + a
+--R +
+--R +--------+
+--R 3 +-----------+ +-+ | 2
+--R ((3a d + 2b c)x + 5a c x)\|- a d + b c \|c \|b x + a
+--R /
+--R 2 2 4 3 2 4 +-----------+ +-+
+--R (8c d x + 16c d x + 8c )\|- a d + b c \|c
+--R Type: Expression(Integer)
+--E 378
+
+--S 379 of 994
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R 2 2 6 3 2 2 4 3 2 2 2
+--R 12a b d x + (24a d + 24a b c d)x + (48a c d + 12a b c )x
+--R +
+--R 3 2
+--R 24a c
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|a \|b x + a
+--R +
+--R 2 2 2 8 3 2 2 2 6
+--R - 3a b d x + (- 24a b d - 6a b c d)x
+--R +
+--R 4 2 3 2 2 2 4 4 3 2 2
+--R (- 24a d - 48a b c d - 3a b c )x + (- 48a c d - 24a b c )x
+--R +
+--R 4 2
+--R - 24a c
+--R *
+--R log
+--R +--------------+
+--R 2 | 2 +-+
+--R ((- 2a d + 4b c)x + 2a c)\|- a c d + b c \|a
+--R +
+--R 2 2 3 2 2
+--R (2a b c d - 2b c )x + (4a c d - 4a b c )x
+--R *
+--R +--------+
+--R | 2
+--R \|b x + a
+--R +
+--R 2 2 3 2 2 +-+
+--R ((- 4a b c d + 4b c )x + (- 4a c d + 4a b c )x)\|a
+--R +
+--R +--------------+
+--R 2 4 2 2 2 | 2
+--R ((a b d - 2b c)x + (2a d - 5a b c)x - 2a c)\|- a c d + b c
+--R /
+--R +--------+
+--R 2 +-+ | 2 4 2
+--R (2d x + 2c)\|a \|b x + a - b d x + (- 2a d - b c)x - 2a c
+--R +
+--R 2 3 7 2 2 5
+--R (- 6a b d - 4b c)x + (- 48a b d - 42a b c)x
+--R +
+--R 3 2 3 3
+--R (- 48a d - 112a b c)x - 80a c x
+--R *
+--R +--------------+ +--------+
+--R | 2 | 2
+--R \|- a c d + b c \|b x + a
+--R +
+--R 2 3 7 2 2 5 3 2 3
+--R (24a b d + 16b c)x + (72a b d + 88a b c)x + (48a d + 152a b c)x
+--R +
+--R 3
+--R 80a c x
+--R *
+--R +--------------+
+--R | 2 +-+
+--R \|- a c d + b c \|a
+--R /
+--R 2 2 6 2 2 3 4 3 4 2
+--R 64b c d x + (128a c d + 128b c d)x + (256a c d + 64b c )x
+--R +
+--R 4
+--R 128a c
+--R *
+--R +--------------+ +--------+
+--R | 2 +-+ | 2
+--R \|- a c d + b c \|a \|b x + a
+--R +
+--R 2 2 2 8 2 2 2 3 6
+--R - 16b c d x + (- 128a b c d - 32b c d)x
+--R +
+--R 2 2 2 3 2 4 4 2 3 4 2
+--R (- 128a c d - 256a b c d - 16b c )x + (- 256a c d - 128a b c )x
+--R +
+--R 2 4
+--R - 128a c
+--R *
+--R +--------------+
+--R | 2
+--R \|- a c d + b c
+--R ,
+--R
+--R 2 2 6 3 2 2 4 3 2 2 2
+--R 12a b d x + (24a d + 24a b c d)x + (48a c d + 12a b c )x
+--R +
+--R 3 2
+--R 24a c
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|a \|b x + a
+--R +
+--R 2 2 2 8 3 2 2 2 6
+--R - 3a b d x + (- 24a b d - 6a b c d)x
+--R +
+--R 4 2 3 2 2 2 4 4 3 2 2
+--R (- 24a d - 48a b c d - 3a b c )x + (- 48a c d - 24a b c )x
+--R +
+--R 4 2
+--R - 24a c
+--R *
+--R +--------+
+--R 2 | 2 2 +-+
+--R ((a d - b c)x + a c)\|b x + a + (- a d x - a c)\|a
+--R atan(-------------------------------------------------------)
+--R +------------+
+--R 3 | 2
+--R b x \|a c d - b c
+--R +
+--R 2 2 6 3 2 2 4 3 2 2 2
+--R 12a b d x + (24a d + 24a b c d)x + (48a c d + 12a b c )x
+--R +
+--R 3 2
+--R 24a c
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|a \|b x + a
+--R +
+--R 2 2 2 8 3 2 2 2 6
+--R - 3a b d x + (- 24a b d - 6a b c d)x
+--R +
+--R 4 2 3 2 2 2 4 4 3 2 2
+--R (- 24a d - 48a b c d - 3a b c )x + (- 48a c d - 24a b c )x
+--R +
+--R 4 2
+--R - 24a c
+--R *
+--R +------------+
+--R +-+ | 2
+--R \|a \|a c d - b c
+--R atan(-------------------)
+--R (a d - b c)x
+--R +
+--R 2 3 7 2 2 5
+--R (- 3a b d - 2b c)x + (- 24a b d - 21a b c)x
+--R +
+--R 3 2 3 3
+--R (- 24a d - 56a b c)x - 40a c x
+--R *
+--R +------------+ +--------+
+--R | 2 | 2
+--R \|a c d - b c \|b x + a
+--R +
+--R 2 3 7 2 2 5 3 2 3
+--R (12a b d + 8b c)x + (36a b d + 44a b c)x + (24a d + 76a b c)x
+--R +
+--R 3
+--R 40a c x
+--R *
+--R +------------+
+--R +-+ | 2
+--R \|a \|a c d - b c
+--R /
+--R 2 2 6 2 2 3 4 3 4 2
+--R 32b c d x + (64a c d + 64b c d)x + (128a c d + 32b c )x
+--R +
+--R 4
+--R 64a c
+--R *
+--R +------------+ +--------+
+--R +-+ | 2 | 2
+--R \|a \|a c d - b c \|b x + a
+--R +
+--R 2 2 2 8 2 2 2 3 6
+--R - 8b c d x + (- 64a b c d - 16b c d)x
+--R +
+--R 2 2 2 3 2 4 4 2 3 4 2
+--R (- 64a c d - 128a b c d - 8b c )x + (- 128a c d - 64a b c )x
+--R +
+--R 2 4
+--R - 64a c
+--R *
+--R +------------+
+--R | 2
+--R \|a c d - b c
+--R ]
+--R Type: Union(List(Expression(Integer)),...)
+--E 379
+
+--S 380 of 994
+m0a:=a0.1-r0
+--R
+--R
+--R (4)
+--R 2 +-----------+ +-+
+--R 3a \|- a d + b c \|c
+--R *
+--R log
+--R +--------------+
+--R 2 | 2 +-+
+--R ((- 2a d + 4b c)x + 2a c)\|- a c d + b c \|a
+--R +
+--R 2 2 3 2 2
+--R (2a b c d - 2b c )x + (4a c d - 4a b c )x
+--R *
+--R +--------+
+--R | 2
+--R \|b x + a
+--R +
+--R 2 2 3 2 2 +-+
+--R ((- 4a b c d + 4b c )x + (- 4a c d + 4a b c )x)\|a
+--R +
+--R +--------------+
+--R 2 4 2 2 2 | 2
+--R ((a b d - 2b c)x + (2a d - 5a b c)x - 2a c)\|- a c d + b c
+--R /
+--R +--------+
+--R 2 +-+ | 2 4 2
+--R (2d x + 2c)\|a \|b x + a - b d x + (- 2a d - b c)x - 2a c
+--R +
+--R +--------------+ +-----------+
+--R 2 | 2 x\|- a d + b c
+--R - 6a \|- a c d + b c atanh(---------------)
+--R +--------+
+--R +-+ | 2
+--R \|c \|b x + a
+--R /
+--R +--------------+
+--R 2 | 2 +-----------+ +-+
+--R 16c \|- a c d + b c \|- a d + b c \|c
+--R Type: Expression(Integer)
+--E 380
+
+--S 381 of 994
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 381
+
+--S 382 of 994
+m0b:=a0.2-r0
+--R
+--R
+--R (6)
+--R +------------+ +-----------+
+--R 2 | 2 x\|- a d + b c
+--R - 3a \|a c d - b c atanh(---------------)
+--R +--------+
+--R +-+ | 2
+--R \|c \|b x + a
+--R +
+--R 2 +-----------+ +-+
+--R 3a \|- a d + b c \|c
+--R *
+--R +--------+
+--R 2 | 2 2 +-+
+--R ((a d - b c)x + a c)\|b x + a + (- a d x - a c)\|a
+--R atan(-------------------------------------------------------)
+--R +------------+
+--R 3 | 2
+--R b x \|a c d - b c
+--R +
+--R +------------+
+--R +-+ | 2
+--R 2 +-----------+ +-+ \|a \|a c d - b c
+--R 3a \|- a d + b c \|c atan(-------------------)
+--R (a d - b c)x
+--R /
+--R +------------+
+--R 2 +-----------+ +-+ | 2
+--R 8c \|- a d + b c \|c \|a c d - b c
+--R Type: Expression(Integer)
+--E 382
+
+--S 383 of 994
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 383
+
+)clear all
+
+--S 384 of 994
+t0:=(a+b*x^2)^(3/2)/(c+d*x^2)^4
+--R
+--R
+--R +--------+
+--R 2 | 2
+--R (b x + a)\|b x + a
+--R (1) ---------------------------------------
+--R 4 8 3 6 2 2 4 3 2 4
+--R d x + 4c d x + 6c d x + 4c d x + c
+--R Type: Expression(Integer)
+--E 384
+
+--S 385 of 994
+r0:=1/16*a^2*(6*b*c-5*a*d)*atanh(x*sqrt(b*c-a*d)/(sqrt(c)*_
+ sqrt(a+b*x^2)))/(c^(7/2)*(b*c-a*d)^(3/2))-1/6*(b*c-a*d)*x*_
+ sqrt(a+b*x^2)/(c*d*(c+d*x^2)^3)+1/24*(2*b*c+5*a*d)*x*_
+ sqrt(a+b*x^2)/(c^2*d*(c+d*x^2)^2)+1/48*(4*b^2*c^2+8*a*b*c*_
+ d-15*a^2*d^2)*x*sqrt(a+b*x^2)/(c^3*d*(b*c-a*d)*(c+d*x^2))
+--R
+--R
+--R (2)
+--R 3 4 2 3 6 3 3 2 2 2 4
+--R (15a d - 18a b c d )x + (45a c d - 54a b c d )x
+--R +
+--R 3 2 2 2 3 2 3 3 2 4
+--R (45a c d - 54a b c d)x + 15a c d - 18a b c
+--R *
+--R +-----------+
+--R x\|- a d + b c
+--R atanh(---------------)
+--R +--------+
+--R +-+ | 2
+--R \|c \|b x + a
+--R +
+--R 2 3 2 2 2 5 2 2 2 2 3 3
+--R (15a d - 8a b c d - 4b c d)x + (40a c d - 22a b c d - 12b c )x
+--R +
+--R 2 2 3
+--R (33a c d - 30a b c )x
+--R *
+--R +--------+
+--R +-----------+ +-+ | 2
+--R \|- a d + b c \|c \|b x + a
+--R /
+--R 3 4 4 3 6 4 3 5 2 4
+--R (48a c d - 48b c d )x + (144a c d - 144b c d )x
+--R +
+--R 5 2 6 2 6 7
+--R (144a c d - 144b c d)x + 48a c d - 48b c
+--R *
+--R +-----------+ +-+
+--R \|- a d + b c \|c
+--R Type: Expression(Integer)
+--E 385
+
+--S 386 of 994
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R 3 2 4 2 3 3 10
+--R (90a b d - 108a b c d )x
+--R +
+--R 4 4 3 2 3 2 3 2 2 8
+--R (480a b d - 306a b c d - 324a b c d )x
+--R +
+--R 5 4 4 3 3 2 2 2 2 3 3 6
+--R (480a d + 864a b c d - 1458a b c d - 324a b c d)x
+--R +
+--R 5 3 4 2 2 3 2 3 2 3 4 4
+--R (1440a c d - 288a b c d - 1638a b c d - 108a b c )x
+--R +
+--R 5 2 2 4 3 3 2 4 2 5 3 4 4
+--R (1440a c d - 1248a b c d - 576a b c )x + 480a c d - 576a b c
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|a \|b x + a
+--R +
+--R 3 3 4 2 4 3 12
+--R (- 15a b d + 18a b c d )x
+--R +
+--R 4 2 4 3 3 3 2 4 2 2 10
+--R (- 270a b d + 279a b c d + 54a b c d )x
+--R +
+--R 5 4 4 2 3 3 3 2 2 2 4 3 8
+--R (- 720a b d + 54a b c d + 927a b c d + 54a b c d)x
+--R +
+--R 6 4 5 3 4 2 2 2 3 3 3 2 4 4 6
+--R (- 480a d - 1584a b c d + 1782a b c d + 957a b c d + 18a b c )x
+--R +
+--R 6 3 5 2 2 4 2 3 3 3 4 4
+--R (- 1440a c d - 432a b c d + 2322a b c d + 324a b c )x
+--R +
+--R 6 2 2 5 3 4 2 4 2 6 3 5 4
+--R (- 1440a c d + 1008a b c d + 864a b c )x - 480a c d + 576a b c
+--R *
+--R log
+--R +--------------+
+--R 2 | 2 +-+
+--R ((- 2a d + 4b c)x + 2a c)\|- a c d + b c \|a
+--R +
+--R 2 2 3 2 2
+--R (2a b c d - 2b c )x + (4a c d - 4a b c )x
+--R *
+--R +--------+
+--R | 2
+--R \|b x + a
+--R +
+--R 2 2 3 2 2 +-+
+--R ((- 4a b c d + 4b c )x + (- 4a c d + 4a b c )x)\|a
+--R +
+--R +--------------+
+--R 2 4 2 2 2 | 2
+--R ((a b d - 2b c)x + (2a d - 5a b c)x - 2a c)\|- a c d + b c
+--R /
+--R +--------+
+--R 2 +-+ | 2 4 2
+--R (2d x + 2c)\|a \|b x + a - b d x + (- 2a d - b c)x - 2a c
+--R +
+--R 2 3 3 4 2 5 2 11
+--R (- 30a b d + 16a b c d + 8b c d)x
+--R +
+--R 3 2 3 2 3 2 4 2 5 3 9
+--R (- 540a b d + 208a b c d + 188a b c d + 24b c )x
+--R +
+--R 4 3 3 2 2 2 3 2 4 3 7
+--R (- 1440a b d - 672a b c d + 1110a b c d + 492a b c )x
+--R +
+--R 5 3 4 2 3 2 2 2 3 3 5
+--R (- 960a d - 3328a b c d + 1180a b c d + 2232a b c )x
+--R +
+--R 5 2 4 2 3 2 3 3
+--R (- 2560a c d - 1760a b c d + 3648a b c )x
+--R +
+--R 5 2 4 3
+--R (- 2112a c d + 1920a b c )x
+--R *
+--R +--------------+ +--------+
+--R | 2 | 2
+--R \|- a c d + b c \|b x + a
+--R +
+--R 2 3 3 4 2 5 2 11
+--R (180a b d - 96a b c d - 48b c d)x
+--R +
+--R 3 2 3 2 3 2 4 2 5 3 9
+--R (1140a b d - 128a b c d - 568a b c d - 144b c )x
+--R +
+--R 4 3 3 2 2 2 3 2 4 3 7
+--R (1920a b d + 2016a b c d - 1788a b c d - 1272a b c )x
+--R +
+--R 5 3 4 2 3 2 2 2 3 3 5
+--R (960a d + 4608a b c d - 564a b c d - 3816a b c )x
+--R +
+--R 5 2 4 2 3 2 3 3 5 2 4 3
+--R (2560a c d + 2816a b c d - 4608a b c )x + (2112a c d - 1920a b c )x
+--R *
+--R +--------------+
+--R | 2 +-+
+--R \|- a c d + b c \|a
+--R /
+--R 2 3 4 3 4 3 10
+--R (576a b c d - 576b c d )x
+--R +
+--R 2 3 4 2 4 3 3 5 2 8
+--R (3072a b c d - 1344a b c d - 1728b c d )x
+--R +
+--R 3 3 4 2 4 3 2 5 2 3 6 6
+--R (3072a c d + 6144a b c d - 7488a b c d - 1728b c d)x
+--R +
+--R 3 4 3 2 6 3 7 4
+--R (9216a c d - 8640a b c d - 576b c )x
+--R +
+--R 3 5 2 2 6 2 7 2 3 6 2 7
+--R (9216a c d - 6144a b c d - 3072a b c )x + 3072a c d - 3072a b c
+--R *
+--R +--------------+ +--------+
+--R | 2 +-+ | 2
+--R \|- a c d + b c \|a \|b x + a
+--R +
+--R 3 3 4 4 4 3 12
+--R (- 96a b c d + 96b c d )x
+--R +
+--R 2 2 3 4 3 4 3 4 5 2 10
+--R (- 1728a b c d + 1440a b c d + 288b c d )x
+--R +
+--R 3 3 4 2 2 4 3 3 5 2 4 6 8
+--R (- 4608a b c d - 576a b c d + 4896a b c d + 288b c d)x
+--R +
+--R 4 3 4 3 4 3 2 2 5 2 3 6
+--R - 3072a c d - 10752a b c d + 8640a b c d + 5088a b c d
+--R +
+--R 4 7
+--R 96b c
+--R *
+--R 6
+--R x
+--R +
+--R 4 4 3 3 5 2 2 2 6 3 7 4
+--R (- 9216a c d - 4608a b c d + 12096a b c d + 1728a b c )x
+--R +
+--R 4 5 2 3 6 2 2 7 2 4 6 3 7
+--R (- 9216a c d + 4608a b c d + 4608a b c )x - 3072a c d + 3072a b c
+--R *
+--R +--------------+
+--R | 2
+--R \|- a c d + b c
+--R ,
+--R
+--R 3 2 4 2 3 3 10
+--R (90a b d - 108a b c d )x
+--R +
+--R 4 4 3 2 3 2 3 2 2 8
+--R (480a b d - 306a b c d - 324a b c d )x
+--R +
+--R 5 4 4 3 3 2 2 2 2 3 3 6
+--R (480a d + 864a b c d - 1458a b c d - 324a b c d)x
+--R +
+--R 5 3 4 2 2 3 2 3 2 3 4 4
+--R (1440a c d - 288a b c d - 1638a b c d - 108a b c )x
+--R +
+--R 5 2 2 4 3 3 2 4 2 5 3 4 4
+--R (1440a c d - 1248a b c d - 576a b c )x + 480a c d - 576a b c
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|a \|b x + a
+--R +
+--R 3 3 4 2 4 3 12
+--R (- 15a b d + 18a b c d )x
+--R +
+--R 4 2 4 3 3 3 2 4 2 2 10
+--R (- 270a b d + 279a b c d + 54a b c d )x
+--R +
+--R 5 4 4 2 3 3 3 2 2 2 4 3 8
+--R (- 720a b d + 54a b c d + 927a b c d + 54a b c d)x
+--R +
+--R 6 4 5 3 4 2 2 2 3 3 3 2 4 4 6
+--R (- 480a d - 1584a b c d + 1782a b c d + 957a b c d + 18a b c )x
+--R +
+--R 6 3 5 2 2 4 2 3 3 3 4 4
+--R (- 1440a c d - 432a b c d + 2322a b c d + 324a b c )x
+--R +
+--R 6 2 2 5 3 4 2 4 2 6 3 5 4
+--R (- 1440a c d + 1008a b c d + 864a b c )x - 480a c d + 576a b c
+--R *
+--R +--------+
+--R 2 | 2 2 +-+
+--R ((a d - b c)x + a c)\|b x + a + (- a d x - a c)\|a
+--R atan(-------------------------------------------------------)
+--R +------------+
+--R 3 | 2
+--R b x \|a c d - b c
+--R +
+--R 3 2 4 2 3 3 10
+--R (90a b d - 108a b c d )x
+--R +
+--R 4 4 3 2 3 2 3 2 2 8
+--R (480a b d - 306a b c d - 324a b c d )x
+--R +
+--R 5 4 4 3 3 2 2 2 2 3 3 6
+--R (480a d + 864a b c d - 1458a b c d - 324a b c d)x
+--R +
+--R 5 3 4 2 2 3 2 3 2 3 4 4
+--R (1440a c d - 288a b c d - 1638a b c d - 108a b c )x
+--R +
+--R 5 2 2 4 3 3 2 4 2 5 3 4 4
+--R (1440a c d - 1248a b c d - 576a b c )x + 480a c d - 576a b c
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|a \|b x + a
+--R +
+--R 3 3 4 2 4 3 12
+--R (- 15a b d + 18a b c d )x
+--R +
+--R 4 2 4 3 3 3 2 4 2 2 10
+--R (- 270a b d + 279a b c d + 54a b c d )x
+--R +
+--R 5 4 4 2 3 3 3 2 2 2 4 3 8
+--R (- 720a b d + 54a b c d + 927a b c d + 54a b c d)x
+--R +
+--R 6 4 5 3 4 2 2 2 3 3 3 2 4 4 6
+--R (- 480a d - 1584a b c d + 1782a b c d + 957a b c d + 18a b c )x
+--R +
+--R 6 3 5 2 2 4 2 3 3 3 4 4
+--R (- 1440a c d - 432a b c d + 2322a b c d + 324a b c )x
+--R +
+--R 6 2 2 5 3 4 2 4 2 6 3 5 4
+--R (- 1440a c d + 1008a b c d + 864a b c )x - 480a c d + 576a b c
+--R *
+--R +------------+
+--R +-+ | 2
+--R \|a \|a c d - b c
+--R atan(-------------------)
+--R (a d - b c)x
+--R +
+--R 2 3 3 4 2 5 2 11
+--R (- 15a b d + 8a b c d + 4b c d)x
+--R +
+--R 3 2 3 2 3 2 4 2 5 3 9
+--R (- 270a b d + 104a b c d + 94a b c d + 12b c )x
+--R +
+--R 4 3 3 2 2 2 3 2 4 3 7
+--R (- 720a b d - 336a b c d + 555a b c d + 246a b c )x
+--R +
+--R 5 3 4 2 3 2 2 2 3 3 5
+--R (- 480a d - 1664a b c d + 590a b c d + 1116a b c )x
+--R +
+--R 5 2 4 2 3 2 3 3
+--R (- 1280a c d - 880a b c d + 1824a b c )x
+--R +
+--R 5 2 4 3
+--R (- 1056a c d + 960a b c )x
+--R *
+--R +------------+ +--------+
+--R | 2 | 2
+--R \|a c d - b c \|b x + a
+--R +
+--R 2 3 3 4 2 5 2 11
+--R (90a b d - 48a b c d - 24b c d)x
+--R +
+--R 3 2 3 2 3 2 4 2 5 3 9
+--R (570a b d - 64a b c d - 284a b c d - 72b c )x
+--R +
+--R 4 3 3 2 2 2 3 2 4 3 7
+--R (960a b d + 1008a b c d - 894a b c d - 636a b c )x
+--R +
+--R 5 3 4 2 3 2 2 2 3 3 5
+--R (480a d + 2304a b c d - 282a b c d - 1908a b c )x
+--R +
+--R 5 2 4 2 3 2 3 3 5 2 4 3
+--R (1280a c d + 1408a b c d - 2304a b c )x + (1056a c d - 960a b c )x
+--R *
+--R +------------+
+--R +-+ | 2
+--R \|a \|a c d - b c
+--R /
+--R 2 3 4 3 4 3 10
+--R (288a b c d - 288b c d )x
+--R +
+--R 2 3 4 2 4 3 3 5 2 8
+--R (1536a b c d - 672a b c d - 864b c d )x
+--R +
+--R 3 3 4 2 4 3 2 5 2 3 6 6
+--R (1536a c d + 3072a b c d - 3744a b c d - 864b c d)x
+--R +
+--R 3 4 3 2 6 3 7 4
+--R (4608a c d - 4320a b c d - 288b c )x
+--R +
+--R 3 5 2 2 6 2 7 2 3 6 2 7
+--R (4608a c d - 3072a b c d - 1536a b c )x + 1536a c d - 1536a b c
+--R *
+--R +------------+ +--------+
+--R +-+ | 2 | 2
+--R \|a \|a c d - b c \|b x + a
+--R +
+--R 3 3 4 4 4 3 12
+--R (- 48a b c d + 48b c d )x
+--R +
+--R 2 2 3 4 3 4 3 4 5 2 10
+--R (- 864a b c d + 720a b c d + 144b c d )x
+--R +
+--R 3 3 4 2 2 4 3 3 5 2 4 6 8
+--R (- 2304a b c d - 288a b c d + 2448a b c d + 144b c d)x
+--R +
+--R 4 3 4 3 4 3 2 2 5 2 3 6
+--R - 1536a c d - 5376a b c d + 4320a b c d + 2544a b c d
+--R +
+--R 4 7
+--R 48b c
+--R *
+--R 6
+--R x
+--R +
+--R 4 4 3 3 5 2 2 2 6 3 7 4
+--R (- 4608a c d - 2304a b c d + 6048a b c d + 864a b c )x
+--R +
+--R 4 5 2 3 6 2 2 7 2 4 6 3 7
+--R (- 4608a c d + 2304a b c d + 2304a b c )x - 1536a c d + 1536a b c
+--R *
+--R +------------+
+--R | 2
+--R \|a c d - b c
+--R ]
+--R Type: Union(List(Expression(Integer)),...)
+--E 386
+
+--S 387 of 994
+m0a:=a0.1-r0
+--R
+--R
+--R (4)
+--R 3 2 +-----------+ +-+
+--R (5a d - 6a b c)\|- a d + b c \|c
+--R *
+--R log
+--R +--------------+
+--R 2 | 2 +-+
+--R ((- 2a d + 4b c)x + 2a c)\|- a c d + b c \|a
+--R +
+--R 2 2 3 2 2
+--R (2a b c d - 2b c )x + (4a c d - 4a b c )x
+--R *
+--R +--------+
+--R | 2
+--R \|b x + a
+--R +
+--R 2 2 3 2 2 +-+
+--R ((- 4a b c d + 4b c )x + (- 4a c d + 4a b c )x)\|a
+--R +
+--R +--------------+
+--R 2 4 2 2 2 | 2
+--R ((a b d - 2b c)x + (2a d - 5a b c)x - 2a c)\|- a c d + b c
+--R /
+--R +--------+
+--R 2 +-+ | 2 4 2
+--R (2d x + 2c)\|a \|b x + a - b d x + (- 2a d - b c)x - 2a c
+--R +
+--R +--------------+ +-----------+
+--R 3 2 | 2 x\|- a d + b c
+--R (- 10a d + 12a b c)\|- a c d + b c atanh(---------------)
+--R +--------+
+--R +-+ | 2
+--R \|c \|b x + a
+--R /
+--R +--------------+
+--R 3 4 | 2 +-----------+ +-+
+--R (32a c d - 32b c )\|- a c d + b c \|- a d + b c \|c
+--R Type: Expression(Integer)
+--E 387
+
+--S 388 of 994
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 388
+
+--S 389 of 994
+m0b:=a0.2-r0
+--R
+--R
+--R (6)
+--R +------------+ +-----------+
+--R 3 2 | 2 x\|- a d + b c
+--R (- 5a d + 6a b c)\|a c d - b c atanh(---------------)
+--R +--------+
+--R +-+ | 2
+--R \|c \|b x + a
+--R +
+--R 3 2 +-----------+ +-+
+--R (5a d - 6a b c)\|- a d + b c \|c
+--R *
+--R +--------+
+--R 2 | 2 2 +-+
+--R ((a d - b c)x + a c)\|b x + a + (- a d x - a c)\|a
+--R atan(-------------------------------------------------------)
+--R +------------+
+--R 3 | 2
+--R b x \|a c d - b c
+--R +
+--R +------------+
+--R +-+ | 2
+--R 3 2 +-----------+ +-+ \|a \|a c d - b c
+--R (5a d - 6a b c)\|- a d + b c \|c atan(-------------------)
+--R (a d - b c)x
+--R /
+--R +------------+
+--R 3 4 +-----------+ +-+ | 2
+--R (16a c d - 16b c )\|- a d + b c \|c \|a c d - b c
+--R Type: Expression(Integer)
+--E 389
+
+--S 390 of 994
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 390
+
+)clear all
+
+--S 391 of 994
+t0:=(a+b*x^2)^(3/2)/(c+d*x^2)^5
+--R
+--R
+--R +--------+
+--R 2 | 2
+--R (b x + a)\|b x + a
+--R (1) ----------------------------------------------------
+--R 5 10 4 8 2 3 6 3 2 4 4 2 5
+--R d x + 5c d x + 10c d x + 10c d x + 5c d x + c
+--R Type: Expression(Integer)
+--E 391
+
+--S 392 of 994
+r0:=1/128*a^2*(48*b^2*c^2-80*a*b*c*d+35*a^2*d^2)*atanh(x*sqrt(b*c-_
+ a*d)/(sqrt(c)*sqrt(a+b*x^2)))/(c^(9/2)*(b*c-a*d)^(5/2))-_
+ 1/8*(b*c-a*d)*x*sqrt(a+b*x^2)/(c*d*(c+d*x^2)^4)+1/48*(2*b*c+_
+ 7*a*d)*x*sqrt(a+b*x^2)/(c^2*d*(c+d*x^2)^3)+1/192*(8*b^2*c^2+_
+ 24*a*b*c*d-35*a^2*d^2)*x*sqrt(a+b*x^2)/(c^3*d*(b*c-a*d)*(c+_
+ d*x^2)^2)+1/384*(16*b^3*c^3+40*a*b^2*c^2*d-170*a^2*b*c*d^2+_
+ 105*a^3*d^3)*x*sqrt(a+b*x^2)/(c^4*d*(b*c-a*d)^2*(c+d*x^2))
+--R
+--R
+--R (2)
+--R 4 6 3 5 2 2 2 4 8
+--R (105a d - 240a b c d + 144a b c d )x
+--R +
+--R 4 5 3 2 4 2 2 3 3 6
+--R (420a c d - 960a b c d + 576a b c d )x
+--R +
+--R 4 2 4 3 3 3 2 2 4 2 4
+--R (630a c d - 1440a b c d + 864a b c d )x
+--R +
+--R 4 3 3 3 4 2 2 2 5 2 4 4 2 3 5
+--R (420a c d - 960a b c d + 576a b c d)x + 105a c d - 240a b c d
+--R +
+--R 2 2 6
+--R 144a b c
+--R *
+--R +-----------+
+--R x\|- a d + b c
+--R atanh(---------------)
+--R +--------+
+--R +-+ | 2
+--R \|c \|b x + a
+--R +
+--R 3 5 2 4 2 2 3 3 3 2 7
+--R (105a d - 170a b c d + 40a b c d + 16b c d )x
+--R +
+--R 3 4 2 2 3 2 3 2 3 4 5
+--R (385a c d - 628a b c d + 152a b c d + 64b c d)x
+--R +
+--R 3 2 3 2 3 2 2 4 3 5 3
+--R (511a c d - 842a b c d + 208a b c d + 96b c )x
+--R +
+--R 3 3 2 2 4 2 5
+--R (279a c d - 528a b c d + 240a b c )x
+--R *
+--R +--------+
+--R +-----------+ +-+ | 2
+--R \|- a d + b c \|c \|b x + a
+--R /
+--R 2 4 6 5 5 2 6 4 8
+--R (384a c d - 768a b c d + 384b c d )x
+--R +
+--R 2 5 5 6 4 2 7 3 6
+--R (1536a c d - 3072a b c d + 1536b c d )x
+--R +
+--R 2 6 4 7 3 2 8 2 4
+--R (2304a c d - 4608a b c d + 2304b c d )x
+--R +
+--R 2 7 3 8 2 2 9 2 2 8 2 9
+--R (1536a c d - 3072a b c d + 1536b c d)x + 384a c d - 768a b c d
+--R +
+--R 2 10
+--R 384b c
+--R *
+--R +-----------+ +-+
+--R \|- a d + b c \|c
+--R Type: Expression(Integer)
+--E 392
+
+--S 393 of 994
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R 4 3 6 3 4 5 2 5 2 4 14
+--R (840a b d - 1920a b c d + 1152a b c d )x
+--R +
+--R 5 2 6 4 3 5 3 4 2 4 2 5 3 3 12
+--R (8400a b d - 15840a b c d + 3840a b c d + 4608a b c d )x
+--R +
+--R 6 6 5 2 5 4 3 2 4 3 4 3 3
+--R 20160a b d - 12480a b c d - 44112a b c d + 34560a b c d
+--R +
+--R 2 5 4 2
+--R 6912a b c d
+--R *
+--R 10
+--R x
+--R +
+--R 7 6 6 5 5 2 2 4 4 3 3 3
+--R 13440a d + 49920a b c d - 115488a b c d - 1248a b c d
+--R +
+--R 3 4 4 2 2 5 5
+--R 61440a b c d + 4608a b c d
+--R *
+--R 8
+--R x
+--R +
+--R 7 5 6 2 4 5 2 3 3 4 3 4 2
+--R 53760a c d - 1920a b c d - 169152a b c d + 89928a b c d
+--R +
+--R 3 4 5 2 5 6
+--R 44160a b c d + 1152a b c
+--R *
+--R 6
+--R x
+--R +
+--R 7 2 4 6 3 3 5 2 4 2 4 3 5
+--R 80640a c d - 103680a b c d - 65328a b c d + 91392a b c d
+--R +
+--R 3 4 6
+--R 11520a b c
+--R *
+--R 4
+--R x
+--R +
+--R 7 3 3 6 4 2 5 2 5 4 3 6 2
+--R (53760a c d - 102720a b c d + 27648a b c d + 27648a b c )x
+--R +
+--R 7 4 2 6 5 5 2 6
+--R 13440a c d - 30720a b c d + 18432a b c
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|a \|b x + a
+--R +
+--R 4 4 6 3 5 5 2 6 2 4 16
+--R (- 105a b d + 240a b c d - 144a b c d )x
+--R +
+--R 5 3 6 4 4 5 3 5 2 4 2 6 3 3 14
+--R (- 3360a b d + 7260a b c d - 3648a b c d - 576a b c d )x
+--R +
+--R 6 2 6 5 3 5 4 4 2 4 3 5 3 3
+--R - 16800a b d + 24960a b c d + 7050a b c d - 16992a b c d
+--R +
+--R 2 6 4 2
+--R - 864a b c d
+--R *
+--R 12
+--R x
+--R +
+--R 7 6 6 2 5 5 3 2 4 4 4 3 3
+--R - 26880a b d - 5760a b c d + 96576a b c d - 46500a b c d
+--R +
+--R 3 5 4 2 2 6 5
+--R - 26688a b c d - 576a b c d
+--R *
+--R 10
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+--R (30720a b c d - 49152a b c d + 6144a b c d + 12288b c d )x
+--R +
+--R 4 4 6 3 2 5 5 2 3 6 4 4 7 3
+--R 73728a b c d - 24576a b c d - 153600a b c d + 86016a b c d
+--R +
+--R 5 8 2
+--R 18432b c d
+--R *
+--R 10
+--R x
+--R +
+--R 5 4 6 4 5 5 3 2 6 4 2 3 7 3
+--R 49152a c d + 196608a b c d - 356352a b c d - 61440a b c d
+--R +
+--R 4 8 2 5 9
+--R 159744a b c d + 12288b c d
+--R *
+--R 8
+--R x
+--R +
+--R 5 5 5 4 6 4 3 2 7 3 2 3 8 2
+--R 196608a c d + 49152a b c d - 565248a b c d + 199680a b c d
+--R +
+--R 4 9 5 10
+--R 116736a b c d + 3072b c
+--R *
+--R 6
+--R x
+--R +
+--R 5 6 4 4 7 3 3 2 8 2 2 3 9
+--R 294912a c d - 294912a b c d - 264192a b c d + 233472a b c d
+--R +
+--R 4 10
+--R 30720a b c
+--R *
+--R 4
+--R x
+--R +
+--R 5 7 3 4 8 2 3 2 9 2 3 10 2
+--R (196608a c d - 319488a b c d + 49152a b c d + 73728a b c )x
+--R +
+--R 5 8 2 4 9 3 2 10
+--R 49152a c d - 98304a b c d + 49152a b c
+--R *
+--R +------------+ +--------+
+--R +-+ | 2 | 2
+--R \|a \|a c d - b c \|b x + a
+--R +
+--R 2 4 4 6 5 5 5 6 6 4 16
+--R (- 384a b c d + 768a b c d - 384b c d )x
+--R +
+--R 3 3 4 6 2 4 5 5 5 6 4 6 7 3 14
+--R (- 12288a b c d + 23040a b c d - 9216a b c d - 1536b c d )x
+--R +
+--R 4 2 4 6 3 3 5 5 2 4 6 4 5 7 3
+--R - 61440a b c d + 73728a b c d + 34560a b c d - 44544a b c d
+--R +
+--R 6 8 2
+--R - 2304b c d
+--R *
+--R 12
+--R x
+--R +
+--R 5 4 6 4 2 5 5 3 3 6 4
+--R - 98304a b c d - 49152a b c d + 319488a b c d
+--R +
+--R 2 4 7 3 5 8 2 6 9
+--R - 99840a b c d - 70656a b c d - 1536b c d
+--R *
+--R 10
+--R x
+--R +
+--R 6 4 6 5 5 5 4 2 6 4
+--R - 49152a c d - 294912a b c d + 368640a b c d
+--R +
+--R 3 3 7 3 2 4 8 2 5 9 6 10
+--R 294912a b c d - 270720a b c d - 48384a b c d - 384b c
+--R *
+--R 8
+--R x
+--R +
+--R 6 5 5 5 6 4 4 2 7 3
+--R - 196608a c d - 196608a b c d + 737280a b c d
+--R +
+--R 3 3 8 2 2 4 9 5 10
+--R - 110592a b c d - 221184a b c d - 12288a b c
+--R *
+--R 6
+--R x
+--R +
+--R 6 6 4 5 7 3 4 2 8 2
+--R - 294912a c d + 196608a b c d + 430080a b c d
+--R +
+--R 3 3 9 2 4 10
+--R - 270336a b c d - 61440a b c
+--R *
+--R 4
+--R x
+--R +
+--R 6 7 3 5 8 2 3 3 10 2 6 8 2
+--R (- 196608a c d + 294912a b c d - 98304a b c )x - 49152a c d
+--R +
+--R 5 9 4 2 10
+--R 98304a b c d - 49152a b c
+--R *
+--R +------------+
+--R | 2
+--R \|a c d - b c
+--R ]
+--R Type: Union(List(Expression(Integer)),...)
+--E 393
+
+--S 394 of 994
+m0a:=a0.1-r0
+--R
+--R
+--R (4)
+--R 4 2 3 2 2 2 +-----------+ +-+
+--R (35a d - 80a b c d + 48a b c )\|- a d + b c \|c
+--R *
+--R log
+--R +--------------+
+--R 2 | 2 +-+
+--R ((- 2a d + 4b c)x + 2a c)\|- a c d + b c \|a
+--R +
+--R 2 2 3 2 2
+--R (2a b c d - 2b c )x + (4a c d - 4a b c )x
+--R *
+--R +--------+
+--R | 2
+--R \|b x + a
+--R +
+--R 2 2 3 2 2 +-+
+--R ((- 4a b c d + 4b c )x + (- 4a c d + 4a b c )x)\|a
+--R +
+--R +--------------+
+--R 2 4 2 2 2 | 2
+--R ((a b d - 2b c)x + (2a d - 5a b c)x - 2a c)\|- a c d + b c
+--R /
+--R +--------+
+--R 2 +-+ | 2 4 2
+--R (2d x + 2c)\|a \|b x + a - b d x + (- 2a d - b c)x - 2a c
+--R +
+--R +--------------+ +-----------+
+--R 4 2 3 2 2 2 | 2 x\|- a d + b c
+--R (- 70a d + 160a b c d - 96a b c )\|- a c d + b c atanh(---------------)
+--R +--------+
+--R +-+ | 2
+--R \|c \|b x + a
+--R /
+--R +--------------+
+--R 2 4 2 5 2 6 | 2 +-----------+ +-+
+--R (256a c d - 512a b c d + 256b c )\|- a c d + b c \|- a d + b c \|c
+--R Type: Expression(Integer)
+--E 394
+
+--S 395 of 994
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 395
+
+--S 396 of 994
+m0b:=a0.2-r0
+--R
+--R
+--R (6)
+--R +------------+ +-----------+
+--R 4 2 3 2 2 2 | 2 x\|- a d + b c
+--R (- 35a d + 80a b c d - 48a b c )\|a c d - b c atanh(---------------)
+--R +--------+
+--R +-+ | 2
+--R \|c \|b x + a
+--R +
+--R 4 2 3 2 2 2 +-----------+ +-+
+--R (35a d - 80a b c d + 48a b c )\|- a d + b c \|c
+--R *
+--R +--------+
+--R 2 | 2 2 +-+
+--R ((a d - b c)x + a c)\|b x + a + (- a d x - a c)\|a
+--R atan(-------------------------------------------------------)
+--R +------------+
+--R 3 | 2
+--R b x \|a c d - b c
+--R +
+--R +------------+
+--R +-+ | 2
+--R 4 2 3 2 2 2 +-----------+ +-+ \|a \|a c d - b c
+--R (35a d - 80a b c d + 48a b c )\|- a d + b c \|c atan(-------------------)
+--R (a d - b c)x
+--R /
+--R +------------+
+--R 2 4 2 5 2 6 +-----------+ +-+ | 2
+--R (128a c d - 256a b c d + 128b c )\|- a d + b c \|c \|a c d - b c
+--R Type: Expression(Integer)
+--E 396
+
+--S 397 of 994
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 397
+
+)clear all
+
+--S 398 of 994
+t0:=sqrt(1-x^2)/(1+x^2)
+--R
+--R
+--R +--------+
+--R | 2
+--R \|- x + 1
+--R (1) -----------
+--R 2
+--R x + 1
+--R Type: Expression(Integer)
+--E 398
+
+--S 399 of 994
+r0:=-asin(x)+atan(x*sqrt(2)/sqrt(1-x^2))*sqrt(2)
+--R
+--R
+--R +-+
+--R +-+ x\|2
+--R (2) \|2 atan(-----------) - asin(x)
+--R +--------+
+--R | 2
+--R \|- x + 1
+--R Type: Expression(Integer)
+--E 399
+
+--S 400 of 994
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +--------+ +--------+
+--R | 2 2 | 2 2
+--R \|- x + 1 - 1 +-+ (2x + 1)\|- x + 1 - x - 1
+--R 2atan(---------------) - \|2 atan(-----------------------------)
+--R x 3 +-+
+--R x \|2
+--R +
+--R +-+ 1
+--R \|2 atan(-----)
+--R +-+
+--R x\|2
+--R Type: Union(Expression(Integer),...)
+--E 400
+
+--S 401 of 994
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +--------+ +--------+
+--R | 2 2 | 2 2
+--R \|- x + 1 - 1 +-+ (2x + 1)\|- x + 1 - x - 1
+--R 2atan(---------------) - \|2 atan(-----------------------------)
+--R x 3 +-+
+--R x \|2
+--R +
+--R +-+
+--R +-+ x\|2 +-+ 1
+--R - \|2 atan(-----------) + \|2 atan(-----) + asin(x)
+--R +--------+ +-+
+--R | 2 x\|2
+--R \|- x + 1
+--R Type: Expression(Integer)
+--E 401
+
+--S 402 of 994
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 402
+
+)clear all
+
+--S 403 of 994
+t0:=sqrt(1+x^2)/(-1+x^2)
+--R
+--R
+--R +------+
+--R | 2
+--R \|x + 1
+--R (1) ---------
+--R 2
+--R x - 1
+--R Type: Expression(Integer)
+--E 403
+
+--S 404 of 994
+r0:=asinh(x)-atanh(x*sqrt(2)/sqrt(1+x^2))*sqrt(2)
+--R
+--R
+--R +-+
+--R +-+ x\|2
+--R (2) - \|2 atanh(---------) + asinh(x)
+--R +------+
+--R | 2
+--R \|x + 1
+--R Type: Expression(Integer)
+--E 404
+
+--S 405 of 994
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +------+
+--R | 2
+--R - 2log(\|x + 1 - x)
+--R +
+--R +------+
+--R +-+ 3 | 2 2 +-+ 4 2
+--R +-+ (2x\|2 + 2x - 2x)\|x + 1 + (- 2x + 2)\|2 - 2x + x - 3
+--R \|2 log(-------------------------------------------------------------)
+--R +------+
+--R 3 | 2 4 2
+--R (2x - 2x)\|x + 1 - 2x + x + 1
+--R /
+--R 2
+--R Type: Union(Expression(Integer),...)
+--E 405
+
+--S 406 of 994
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +------+
+--R | 2
+--R - 2log(\|x + 1 - x)
+--R +
+--R +------+
+--R +-+ 3 | 2 2 +-+ 4 2
+--R +-+ (2x\|2 + 2x - 2x)\|x + 1 + (- 2x + 2)\|2 - 2x + x - 3
+--R \|2 log(-------------------------------------------------------------)
+--R +------+
+--R 3 | 2 4 2
+--R (2x - 2x)\|x + 1 - 2x + x + 1
+--R +
+--R +-+
+--R +-+ x\|2
+--R 2\|2 atanh(---------) - 2asinh(x)
+--R +------+
+--R | 2
+--R \|x + 1
+--R /
+--R 2
+--R Type: Expression(Integer)
+--E 406
+
+--S 407 of 994
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 407
+
+)clear all
+
+--S 408 of 994
+t0:=sqrt(1-x^2)/(-1+2*x^2)
+--R
+--R
+--R +--------+
+--R | 2
+--R \|- x + 1
+--R (1) -----------
+--R 2
+--R 2x - 1
+--R Type: Expression(Integer)
+--E 408
+
+--S 409 of 994
+r0:=-1/2*asin(x)-1/2*atanh(x/sqrt(1-x^2))
+--R
+--R
+--R x
+--R - atanh(-----------) - asin(x)
+--R +--------+
+--R | 2
+--R \|- x + 1
+--R (2) ------------------------------
+--R 2
+--R Type: Expression(Integer)
+--E 409
+
+--S 410 of 994
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +--------+
+--R | 2 2
+--R (x - 1)\|- x + 1 - x - x + 1
+--R - log(-------------------------------)
+--R 2
+--R x
+--R +
+--R +--------+ +--------+
+--R | 2 2 | 2
+--R (- x - 1)\|- x + 1 - x + x + 1 \|- x + 1 - 1
+--R log(---------------------------------) + 4atan(---------------)
+--R 2 x
+--R x
+--R /
+--R 4
+--R Type: Union(Expression(Integer),...)
+--E 410
+
+--S 411 of 994
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +--------+
+--R | 2 2
+--R (x - 1)\|- x + 1 - x - x + 1
+--R - log(-------------------------------)
+--R 2
+--R x
+--R +
+--R +--------+
+--R | 2 2
+--R (- x - 1)\|- x + 1 - x + x + 1 x
+--R log(---------------------------------) + 2atanh(-----------)
+--R 2 +--------+
+--R x | 2
+--R \|- x + 1
+--R +
+--R +--------+
+--R | 2
+--R \|- x + 1 - 1
+--R 4atan(---------------) + 2asin(x)
+--R x
+--R /
+--R 4
+--R Type: Expression(Integer)
+--E 411
+
+--S 412 of 994
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 412
+
+)clear all
+
+--S 413 of 994
+t0:=(c+d*x^2)^3/(a+b*x^2)^(1/2)
+--R
+--R
+--R 3 6 2 4 2 2 3
+--R d x + 3c d x + 3c d x + c
+--R (1) -----------------------------
+--R +--------+
+--R | 2
+--R \|b x + a
+--R Type: Expression(Integer)
+--E 413
+
+--S 414 of 994
+r0:=1/16*(2*b*c-a*d)*(8*b^2*c^2-8*a*b*c*d+5*a^2*d^2)*atanh(x*sqrt(b)/_
+ sqrt(a+b*x^2))/b^(7/2)+1/48*d*(52*b^2*c^2-52*a*b*c*d+15*a^2*_
+ d^2)*x*sqrt(a+b*x^2)/b^3+1/6*d*x*(c+d*x^2)^2*sqrt(a+b*x^2)/b+_
+ 1/24*d*x*(c*(6*b*c-a*d)+5*d*(2*b*c-a*d)*x^2)*sqrt(a+b*x^2)/b^2
+--R
+--R
+--R (2)
+--R +-+
+--R 3 3 2 2 2 2 3 3 x\|b
+--R (- 15a d + 54a b c d - 72a b c d + 48b c )atanh(-----------)
+--R +--------+
+--R | 2
+--R \|b x + a
+--R +
+--R 2 3 5 3 2 2 3
+--R 8b d x + (- 10a b d + 36b c d )x
+--R +
+--R 2 3 2 2 2
+--R (15a d - 54a b c d + 72b c d)x
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|b \|b x + a
+--R /
+--R 3 +-+
+--R 48b \|b
+--R Type: Expression(Integer)
+--E 414
+
+--S 415 of 994
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R 3 2 3 2 3 2 4 2 5 3 4
+--R (90a b d - 324a b c d + 432a b c d - 288b c )x
+--R +
+--R 4 3 3 2 2 2 3 2 4 3 2
+--R (480a b d - 1728a b c d + 2304a b c d - 1536a b c )x
+--R +
+--R 5 3 4 2 3 2 2 2 3 3
+--R 480a d - 1728a b c d + 2304a b c d - 1536a b c
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|a \|b x + a
+--R +
+--R 3 3 3 2 4 2 5 2 6 3 6
+--R (- 15a b d + 54a b c d - 72a b c d + 48b c )x
+--R +
+--R 4 2 3 3 3 2 2 4 2 5 3 4
+--R (- 270a b d + 972a b c d - 1296a b c d + 864a b c )x
+--R +
+--R 5 3 4 2 2 3 3 2 2 4 3 2 6 3
+--R (- 720a b d + 2592a b c d - 3456a b c d + 2304a b c )x - 480a d
+--R +
+--R 5 2 4 2 2 3 3 3
+--R 1728a b c d - 2304a b c d + 1536a b c
+--R *
+--R +--------+
+--R +-+ +-+ | 2 2 +-+ +-+
+--R (\|a \|b + b x)\|b x + a + (- b x - a)\|b - b x\|a
+--R log(--------------------------------------------------------)
+--R +--------+
+--R +-+ | 2
+--R \|a \|b x + a - a
+--R +
+--R 5 3 11 4 3 5 2 9
+--R - 8b d x + (- 134a b d - 36b c d )x
+--R +
+--R 2 3 3 4 2 5 2 7
+--R (- 219a b d - 594a b c d - 72b c d)x
+--R +
+--R 3 2 3 2 3 2 4 2 5
+--R (- 46a b d - 756a b c d - 1296a b c d)x
+--R +
+--R 4 3 3 2 2 2 3 2 3
+--R (- 400a b d + 1440a b c d - 3456a b c d)x
+--R +
+--R 5 3 4 2 3 2 2
+--R (- 480a d + 1728a b c d - 2304a b c d)x
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|b \|b x + a
+--R +
+--R 5 3 11 4 3 5 2 9
+--R 48b d x + (244a b d + 216b c d )x
+--R +
+--R 2 3 3 4 2 5 2 7
+--R (222a b d + 1044a b c d + 432b c d)x
+--R +
+--R 3 2 3 2 3 2 4 2 5
+--R (186a b d + 252a b c d + 2736a b c d)x
+--R +
+--R 4 3 3 2 2 2 3 2 3
+--R (640a b d - 2304a b c d + 4608a b c d)x
+--R +
+--R 5 3 4 2 3 2 2
+--R (480a d - 1728a b c d + 2304a b c d)x
+--R *
+--R +-+ +-+
+--R \|a \|b
+--R /
+--R +--------+
+--R 5 4 4 2 2 3 +-+ +-+ | 2
+--R (288b x + 1536a b x + 1536a b )\|a \|b \|b x + a
+--R +
+--R 6 6 5 4 2 4 2 3 3 +-+
+--R (- 48b x - 864a b x - 2304a b x - 1536a b )\|b
+--R ,
+--R
+--R 3 2 3 2 3 2 4 2 5 3 4
+--R (- 180a b d + 648a b c d - 864a b c d + 576b c )x
+--R +
+--R 4 3 3 2 2 2 3 2 4 3 2
+--R (- 960a b d + 3456a b c d - 4608a b c d + 3072a b c )x
+--R +
+--R 5 3 4 2 3 2 2 2 3 3
+--R - 960a d + 3456a b c d - 4608a b c d + 3072a b c
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|a \|b x + a
+--R +
+--R 3 3 3 2 4 2 5 2 6 3 6
+--R (30a b d - 108a b c d + 144a b c d - 96b c )x
+--R +
+--R 4 2 3 3 3 2 2 4 2 5 3 4
+--R (540a b d - 1944a b c d + 2592a b c d - 1728a b c )x
+--R +
+--R 5 3 4 2 2 3 3 2 2 4 3 2 6 3
+--R (1440a b d - 5184a b c d + 6912a b c d - 4608a b c )x + 960a d
+--R +
+--R 5 2 4 2 2 3 3 3
+--R - 3456a b c d + 4608a b c d - 3072a b c
+--R *
+--R +--------+
+--R +---+ | 2 +---+ +-+
+--R \|- b \|b x + a - \|- b \|a
+--R atan(------------------------------)
+--R b x
+--R +
+--R 5 3 11 4 3 5 2 9
+--R - 8b d x + (- 134a b d - 36b c d )x
+--R +
+--R 2 3 3 4 2 5 2 7
+--R (- 219a b d - 594a b c d - 72b c d)x
+--R +
+--R 3 2 3 2 3 2 4 2 5
+--R (- 46a b d - 756a b c d - 1296a b c d)x
+--R +
+--R 4 3 3 2 2 2 3 2 3
+--R (- 400a b d + 1440a b c d - 3456a b c d)x
+--R +
+--R 5 3 4 2 3 2 2
+--R (- 480a d + 1728a b c d - 2304a b c d)x
+--R *
+--R +--------+
+--R +---+ | 2
+--R \|- b \|b x + a
+--R +
+--R 5 3 11 4 3 5 2 9
+--R 48b d x + (244a b d + 216b c d )x
+--R +
+--R 2 3 3 4 2 5 2 7
+--R (222a b d + 1044a b c d + 432b c d)x
+--R +
+--R 3 2 3 2 3 2 4 2 5
+--R (186a b d + 252a b c d + 2736a b c d)x
+--R +
+--R 4 3 3 2 2 2 3 2 3
+--R (640a b d - 2304a b c d + 4608a b c d)x
+--R +
+--R 5 3 4 2 3 2 2
+--R (480a d - 1728a b c d + 2304a b c d)x
+--R *
+--R +---+ +-+
+--R \|- b \|a
+--R /
+--R +--------+
+--R 5 4 4 2 2 3 +---+ +-+ | 2
+--R (288b x + 1536a b x + 1536a b )\|- b \|a \|b x + a
+--R +
+--R 6 6 5 4 2 4 2 3 3 +---+
+--R (- 48b x - 864a b x - 2304a b x - 1536a b )\|- b
+--R ]
+--R Type: Union(List(Expression(Integer)),...)
+--E 415
+
+--S 416 of 994
+m0a:=a0.1-r0
+--R
+--R
+--R (4)
+--R 3 3 2 2 2 2 3 3
+--R (5a d - 18a b c d + 24a b c d - 16b c )
+--R *
+--R +--------+
+--R +-+ +-+ | 2 2 +-+ +-+
+--R (\|a \|b + b x)\|b x + a + (- b x - a)\|b - b x\|a
+--R log(--------------------------------------------------------)
+--R +--------+
+--R +-+ | 2
+--R \|a \|b x + a - a
+--R +
+--R +-+
+--R 3 3 2 2 2 2 3 3 x\|b
+--R (5a d - 18a b c d + 24a b c d - 16b c )atanh(-----------)
+--R +--------+
+--R | 2
+--R \|b x + a
+--R /
+--R 3 +-+
+--R 16b \|b
+--R Type: Expression(Integer)
+--E 416
+
+--S 417 of 994
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 417
+
+--S 418 of 994
+m0b:=a0.2-r0
+--R
+--R
+--R (6)
+--R +-+
+--R 3 3 2 2 2 2 3 3 +---+ x\|b
+--R (5a d - 18a b c d + 24a b c d - 16b c )\|- b atanh(-----------)
+--R +--------+
+--R | 2
+--R \|b x + a
+--R +
+--R 3 3 2 2 2 2 3 3 +-+
+--R (- 10a d + 36a b c d - 48a b c d + 32b c )\|b
+--R *
+--R +--------+
+--R +---+ | 2 +---+ +-+
+--R \|- b \|b x + a - \|- b \|a
+--R atan(------------------------------)
+--R b x
+--R /
+--R 3 +---+ +-+
+--R 16b \|- b \|b
+--R Type: Expression(Integer)
+--E 418
+
+--S 419 of 994
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 419
+
+)clear all
+
+--S 420 of 994
+t0:=(c+d*x^2)^2/(a+b*x^2)^(1/2)
+--R
+--R
+--R 2 4 2 2
+--R d x + 2c d x + c
+--R (1) -------------------
+--R +--------+
+--R | 2
+--R \|b x + a
+--R Type: Expression(Integer)
+--E 420
+
+--S 421 of 994
+r0:=1/8*(8*b^2*c^2-8*a*b*c*d+3*a^2*d^2)*atanh(x*sqrt(b)/sqrt(a+b*x^2))/_
+ b^(5/2)+3/8*d*(2*b*c-a*d)*x*sqrt(a+b*x^2)/b^2+1/4*d*x*(c+d*x^2)*_
+ sqrt(a+b*x^2)/b
+--R
+--R
+--R (2)
+--R +-+
+--R 2 2 2 2 x\|b
+--R (3a d - 8a b c d + 8b c )atanh(-----------)
+--R +--------+
+--R | 2
+--R \|b x + a
+--R +
+--R +--------+
+--R 2 3 2 +-+ | 2
+--R (2b d x + (- 3a d + 8b c d)x)\|b \|b x + a
+--R /
+--R 2 +-+
+--R 8b \|b
+--R Type: Expression(Integer)
+--E 421
+
+--S 422 of 994
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R 2 2 2 3 2 2 3 2 2
+--R (12a b d - 32a b c d + 32b c )x + 24a d - 64a b c d
+--R +
+--R 2 2
+--R 64a b c
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|a \|b x + a
+--R +
+--R 2 2 2 3 4 2 4
+--R (- 3a b d + 8a b c d - 8b c )x
+--R +
+--R 3 2 2 2 3 2 2 4 2 3 2 2 2
+--R (- 24a b d + 64a b c d - 64a b c )x - 24a d + 64a b c d - 64a b c
+--R *
+--R +--------+
+--R +-+ +-+ | 2 2 +-+ +-+
+--R (\|a \|b - b x)\|b x + a + (- b x - a)\|b + b x\|a
+--R log(--------------------------------------------------------)
+--R +--------+
+--R +-+ | 2
+--R \|a \|b x + a - a
+--R +
+--R 3 2 7 2 2 3 5 2 2 2 3
+--R - 2b d x + (- 13a b d - 8b c d)x + (8a b d - 64a b c d)x
+--R +
+--R 3 2 2
+--R (24a d - 64a b c d)x
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|b \|b x + a
+--R +
+--R 3 2 7 2 2 3 5 2 2 2 3
+--R 8b d x + (12a b d + 32b c d)x + (- 20a b d + 96a b c d)x
+--R +
+--R 3 2 2
+--R (- 24a d + 64a b c d)x
+--R *
+--R +-+ +-+
+--R \|a \|b
+--R /
+--R +--------+
+--R 3 2 2 +-+ +-+ | 2 4 4 3 2 2 2 +-+
+--R (32b x + 64a b )\|a \|b \|b x + a + (- 8b x - 64a b x - 64a b )\|b
+--R ,
+--R
+--R 2 2 2 3 2 2 3 2 2
+--R (24a b d - 64a b c d + 64b c )x + 48a d - 128a b c d
+--R +
+--R 2 2
+--R 128a b c
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|a \|b x + a
+--R +
+--R 2 2 2 3 4 2 4
+--R (- 6a b d + 16a b c d - 16b c )x
+--R +
+--R 3 2 2 2 3 2 2 4 2 3
+--R (- 48a b d + 128a b c d - 128a b c )x - 48a d + 128a b c d
+--R +
+--R 2 2 2
+--R - 128a b c
+--R *
+--R +--------+
+--R +---+ | 2 +---+ +-+
+--R \|- b \|b x + a - \|- b \|a
+--R atan(------------------------------)
+--R b x
+--R +
+--R 3 2 7 2 2 3 5 2 2 2 3
+--R - 2b d x + (- 13a b d - 8b c d)x + (8a b d - 64a b c d)x
+--R +
+--R 3 2 2
+--R (24a d - 64a b c d)x
+--R *
+--R +--------+
+--R +---+ | 2
+--R \|- b \|b x + a
+--R +
+--R 3 2 7 2 2 3 5 2 2 2 3
+--R 8b d x + (12a b d + 32b c d)x + (- 20a b d + 96a b c d)x
+--R +
+--R 3 2 2
+--R (- 24a d + 64a b c d)x
+--R *
+--R +---+ +-+
+--R \|- b \|a
+--R /
+--R +--------+
+--R 3 2 2 +---+ +-+ | 2
+--R (32b x + 64a b )\|- b \|a \|b x + a
+--R +
+--R 4 4 3 2 2 2 +---+
+--R (- 8b x - 64a b x - 64a b )\|- b
+--R ]
+--R Type: Union(List(Expression(Integer)),...)
+--E 422
+
+--S 423 of 994
+m0a:=a0.1-r0
+--R
+--R
+--R (4)
+--R 2 2 2 2
+--R (3a d - 8a b c d + 8b c )
+--R *
+--R +--------+
+--R +-+ +-+ | 2 2 +-+ +-+
+--R (\|a \|b - b x)\|b x + a + (- b x - a)\|b + b x\|a
+--R log(--------------------------------------------------------)
+--R +--------+
+--R +-+ | 2
+--R \|a \|b x + a - a
+--R +
+--R +-+
+--R 2 2 2 2 x\|b
+--R (- 3a d + 8a b c d - 8b c )atanh(-----------)
+--R +--------+
+--R | 2
+--R \|b x + a
+--R /
+--R 2 +-+
+--R 8b \|b
+--R Type: Expression(Integer)
+--E 423
+
+--S 424 of 994
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 424
+
+--S 425 of 994
+m0b:=a0.2-r0
+--R
+--R
+--R (6)
+--R +-+
+--R 2 2 2 2 +---+ x\|b
+--R (- 3a d + 8a b c d - 8b c )\|- b atanh(-----------)
+--R +--------+
+--R | 2
+--R \|b x + a
+--R +
+--R +--------+
+--R +---+ | 2 +---+ +-+
+--R 2 2 2 2 +-+ \|- b \|b x + a - \|- b \|a
+--R (6a d - 16a b c d + 16b c )\|b atan(------------------------------)
+--R b x
+--R /
+--R 2 +---+ +-+
+--R 8b \|- b \|b
+--R Type: Expression(Integer)
+--E 425
+
+--S 426 of 994
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 426
+
+)clear all
+
+--S 427 of 994
+t0:=(c+d*x^2)/(a+b*x^2)^(1/2)
+--R
+--R
+--R 2
+--R d x + c
+--R (1) -----------
+--R +--------+
+--R | 2
+--R \|b x + a
+--R Type: Expression(Integer)
+--E 427
+
+--S 428 of 994
+r0:=1/2*(2*b*c-a*d)*atanh(x*sqrt(b)/sqrt(a+b*x^2))/b^(3/2)+1/2*d*x*_
+ sqrt(a+b*x^2)/b
+--R
+--R
+--R +-+ +--------+
+--R x\|b +-+ | 2
+--R (- a d + 2b c)atanh(-----------) + d x\|b \|b x + a
+--R +--------+
+--R | 2
+--R \|b x + a
+--R (2) -----------------------------------------------------
+--R +-+
+--R 2b\|b
+--R Type: Expression(Integer)
+--E 428
+
+--S 429 of 994
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R +--------+
+--R +-+ | 2 2 2 2
+--R ((2a d - 4b c)\|a \|b x + a + (- a b d + 2b c)x - 2a d + 4a b c)
+--R *
+--R +--------+
+--R +-+ +-+ | 2 2 +-+ +-+
+--R (\|a \|b + b x)\|b x + a + (- b x - a)\|b - b x\|a
+--R log(--------------------------------------------------------)
+--R +--------+
+--R +-+ | 2
+--R \|a \|b x + a - a
+--R +
+--R +--------+
+--R 3 +-+ | 2 3 +-+ +-+
+--R (- b d x - 2a d x)\|b \|b x + a + (2b d x + 2a d x)\|a \|b
+--R /
+--R +--------+
+--R +-+ +-+ | 2 2 2 +-+
+--R 4b\|a \|b \|b x + a + (- 2b x - 4a b)\|b
+--R ,
+--R
+--R +--------+
+--R +-+ | 2 2 2 2
+--R ((- 4a d + 8b c)\|a \|b x + a + (2a b d - 4b c)x + 4a d - 8a b c)
+--R *
+--R +--------+
+--R +---+ | 2 +---+ +-+
+--R \|- b \|b x + a - \|- b \|a
+--R atan(------------------------------)
+--R b x
+--R +
+--R +--------+
+--R 3 +---+ | 2 3 +---+ +-+
+--R (- b d x - 2a d x)\|- b \|b x + a + (2b d x + 2a d x)\|- b \|a
+--R /
+--R +--------+
+--R +---+ +-+ | 2 2 2 +---+
+--R 4b\|- b \|a \|b x + a + (- 2b x - 4a b)\|- b
+--R ]
+--R Type: Union(List(Expression(Integer)),...)
+--E 429
+
+--S 430 of 994
+m0a:=a0.1-r0
+--R
+--R
+--R (4)
+--R +--------+
+--R +-+ +-+ | 2 2 +-+ +-+
+--R (\|a \|b + b x)\|b x + a + (- b x - a)\|b - b x\|a
+--R (a d - 2b c)log(--------------------------------------------------------)
+--R +--------+
+--R +-+ | 2
+--R \|a \|b x + a - a
+--R +
+--R +-+
+--R x\|b
+--R (a d - 2b c)atanh(-----------)
+--R +--------+
+--R | 2
+--R \|b x + a
+--R /
+--R +-+
+--R 2b\|b
+--R Type: Expression(Integer)
+--E 430
+
+--S 431 of 994
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 431
+
+--S 432 of 994
+m0b:=a0.2-r0
+--R
+--R
+--R (6)
+--R +-+
+--R +---+ x\|b
+--R (a d - 2b c)\|- b atanh(-----------)
+--R +--------+
+--R | 2
+--R \|b x + a
+--R +
+--R +--------+
+--R +---+ | 2 +---+ +-+
+--R +-+ \|- b \|b x + a - \|- b \|a
+--R (- 2a d + 4b c)\|b atan(------------------------------)
+--R b x
+--R /
+--R +---+ +-+
+--R 2b\|- b \|b
+--R Type: Expression(Integer)
+--E 432
+
+--S 433 of 994
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 433
+
+)clear all
+
+--S 434 of 994
+t0:=1/(a+b*x^2)^(1/2)
+--R
+--R
+--R 1
+--R (1) -----------
+--R +--------+
+--R | 2
+--R \|b x + a
+--R Type: Expression(Integer)
+--E 434
+
+--S 435 of 994
+r0:=atanh(x*sqrt(b)/sqrt(a+b*x^2))/sqrt(b)
+--R
+--R
+--R +-+
+--R x\|b
+--R atanh(-----------)
+--R +--------+
+--R | 2
+--R \|b x + a
+--R (2) ------------------
+--R +-+
+--R \|b
+--R Type: Expression(Integer)
+--E 435
+
+--S 436 of 994
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +--------+
+--R +-+ +-+ | 2 2 +-+ +-+
+--R (\|a \|b - b x)\|b x + a + (- b x - a)\|b + b x\|a
+--R log(--------------------------------------------------------)
+--R +--------+
+--R +-+ | 2
+--R \|a \|b x + a - a
+--R [-------------------------------------------------------------,
+--R +-+
+--R \|b
+--R +--------+
+--R +---+ | 2 +---+ +-+
+--R \|- b \|b x + a - \|- b \|a
+--R 2atan(------------------------------)
+--R b x
+--R -------------------------------------]
+--R +---+
+--R \|- b
+--R Type: Union(List(Expression(Integer)),...)
+--E 436
+
+--S 437 of 994
+m0a:=a0.1-r0
+--R
+--R
+--R (4)
+--R +--------+
+--R +-+ +-+ | 2 2 +-+ +-+
+--R (\|a \|b - b x)\|b x + a + (- b x - a)\|b + b x\|a
+--R log(--------------------------------------------------------)
+--R +--------+
+--R +-+ | 2
+--R \|a \|b x + a - a
+--R +
+--R +-+
+--R x\|b
+--R - atanh(-----------)
+--R +--------+
+--R | 2
+--R \|b x + a
+--R /
+--R +-+
+--R \|b
+--R Type: Expression(Integer)
+--E 437
+
+--S 438 of 994
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 438
+
+--S 439 of 994
+m0b:=a0.2-r0
+--R
+--R
+--R +--------+
+--R +-+ +---+ | 2 +---+ +-+
+--R +---+ x\|b +-+ \|- b \|b x + a - \|- b \|a
+--R - \|- b atanh(-----------) + 2\|b atan(------------------------------)
+--R +--------+ b x
+--R | 2
+--R \|b x + a
+--R (6) ----------------------------------------------------------------------
+--R +---+ +-+
+--R \|- b \|b
+--R Type: Expression(Integer)
+--E 439
+
+--S 440 of 994
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 440
+
+)clear all
+
+--S 441 of 994
+t0:=1/((a+b*x^2)^(1/2)*(c+d*x^2))
+--R
+--R
+--R 1
+--R (1) ---------------------
+--R +--------+
+--R 2 | 2
+--R (d x + c)\|b x + a
+--R Type: Expression(Integer)
+--E 441
+
+--S 442 of 994
+r0:=atanh(x*sqrt(b*c-a*d)/(sqrt(c)*sqrt(a+b*x^2)))/(sqrt(c)*sqrt(b*c-a*d))
+--R
+--R
+--R +-----------+
+--R x\|- a d + b c
+--R atanh(---------------)
+--R +--------+
+--R +-+ | 2
+--R \|c \|b x + a
+--R (2) ----------------------
+--R +-----------+ +-+
+--R \|- a d + b c \|c
+--R Type: Expression(Integer)
+--E 442
+
+--S 443 of 994
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R log
+--R +--------------+
+--R 2 | 2 +-+
+--R ((- 2a d + 4b c)x + 2a c)\|- a c d + b c \|a
+--R +
+--R 2 2 3 2 2
+--R (2a b c d - 2b c )x + (4a c d - 4a b c )x
+--R *
+--R +--------+
+--R | 2
+--R \|b x + a
+--R +
+--R 2 2 3 2 2 +-+
+--R ((- 4a b c d + 4b c )x + (- 4a c d + 4a b c )x)\|a
+--R +
+--R +--------------+
+--R 2 4 2 2 2 | 2
+--R ((a b d - 2b c)x + (2a d - 5a b c)x - 2a c)\|- a c d + b c
+--R /
+--R +--------+
+--R 2 +-+ | 2 4 2
+--R (2d x + 2c)\|a \|b x + a - b d x + (- 2a d - b c)x - 2a c
+--R /
+--R +--------------+
+--R | 2
+--R 2\|- a c d + b c
+--R ,
+--R
+--R +--------+
+--R 2 | 2 2 +-+
+--R ((a d - b c)x + a c)\|b x + a + (- a d x - a c)\|a
+--R atan(-------------------------------------------------------)
+--R +------------+
+--R 3 | 2
+--R b x \|a c d - b c
+--R +
+--R +------------+
+--R +-+ | 2
+--R \|a \|a c d - b c
+--R atan(-------------------)
+--R (a d - b c)x
+--R /
+--R +------------+
+--R | 2
+--R \|a c d - b c
+--R ]
+--R Type: Union(List(Expression(Integer)),...)
+--E 443
+
+--S 444 of 994
+m0a:=a0.1-r0
+--R
+--R
+--R (4)
+--R +-----------+ +-+
+--R \|- a d + b c \|c
+--R *
+--R log
+--R +--------------+
+--R 2 | 2 +-+
+--R ((- 2a d + 4b c)x + 2a c)\|- a c d + b c \|a
+--R +
+--R 2 2 3 2 2
+--R (2a b c d - 2b c )x + (4a c d - 4a b c )x
+--R *
+--R +--------+
+--R | 2
+--R \|b x + a
+--R +
+--R 2 2 3 2 2 +-+
+--R ((- 4a b c d + 4b c )x + (- 4a c d + 4a b c )x)\|a
+--R +
+--R +--------------+
+--R 2 4 2 2 2 | 2
+--R ((a b d - 2b c)x + (2a d - 5a b c)x - 2a c)\|- a c d + b c
+--R /
+--R +--------+
+--R 2 +-+ | 2 4 2
+--R (2d x + 2c)\|a \|b x + a - b d x + (- 2a d - b c)x - 2a c
+--R +
+--R +--------------+ +-----------+
+--R | 2 x\|- a d + b c
+--R - 2\|- a c d + b c atanh(---------------)
+--R +--------+
+--R +-+ | 2
+--R \|c \|b x + a
+--R /
+--R +--------------+
+--R | 2 +-----------+ +-+
+--R 2\|- a c d + b c \|- a d + b c \|c
+--R Type: Expression(Integer)
+--E 444
+
+--S 445 of 994
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 445
+
+--S 446 of 994
+m0b:=a0.2-r0
+--R
+--R
+--R (6)
+--R +------------+ +-----------+
+--R | 2 x\|- a d + b c
+--R - \|a c d - b c atanh(---------------)
+--R +--------+
+--R +-+ | 2
+--R \|c \|b x + a
+--R +
+--R +-----------+ +-+
+--R \|- a d + b c \|c
+--R *
+--R +--------+
+--R 2 | 2 2 +-+
+--R ((a d - b c)x + a c)\|b x + a + (- a d x - a c)\|a
+--R atan(-------------------------------------------------------)
+--R +------------+
+--R 3 | 2
+--R b x \|a c d - b c
+--R +
+--R +------------+
+--R +-+ | 2
+--R +-----------+ +-+ \|a \|a c d - b c
+--R \|- a d + b c \|c atan(-------------------)
+--R (a d - b c)x
+--R /
+--R +------------+
+--R +-----------+ +-+ | 2
+--R \|- a d + b c \|c \|a c d - b c
+--R Type: Expression(Integer)
+--E 446
+
+--S 447 of 994
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 447
+
+)clear all
+
+--S 448 of 994
+t0:=1/((a+b*x^2)^(1/2)*(c+d*x^2)^2)
+--R
+--R
+--R 1
+--R (1) --------------------------------
+--R +--------+
+--R 2 4 2 2 | 2
+--R (d x + 2c d x + c )\|b x + a
+--R Type: Expression(Integer)
+--E 448
+
+--S 449 of 994
+r0:=1/2*(2*b*c-a*d)*atanh(x*sqrt(b*c-a*d)/(sqrt(c)*sqrt(a+b*x^2)))/_
+ (c^(3/2)*(b*c-a*d)^(3/2))-1/2*d*x*sqrt(a+b*x^2)/(c*(b*c-a*d)*(c+d*x^2))
+--R
+--R
+--R (2)
+--R +-----------+
+--R 2 2 2 x\|- a d + b c
+--R ((a d - 2b c d)x + a c d - 2b c )atanh(---------------)
+--R +--------+
+--R +-+ | 2
+--R \|c \|b x + a
+--R +
+--R +--------+
+--R +-----------+ +-+ | 2
+--R d x\|- a d + b c \|c \|b x + a
+--R /
+--R 2 2 2 2 3 +-----------+ +-+
+--R ((2a c d - 2b c d)x + 2a c d - 2b c )\|- a d + b c \|c
+--R Type: Expression(Integer)
+--E 449
+
+--S 450 of 994
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R +--------+
+--R 2 2 2 +-+ | 2
+--R ((2a d - 4b c d)x + 2a c d - 4b c )\|a \|b x + a
+--R +
+--R 2 2 4 2 2 2 2 2 2
+--R (- a b d + 2b c d)x + (- 2a d + 3a b c d + 2b c )x - 2a c d
+--R +
+--R 2
+--R 4a b c
+--R *
+--R log
+--R +--------------+
+--R 2 | 2 +-+
+--R ((- 2a d + 4b c)x + 2a c)\|- a c d + b c \|a
+--R +
+--R 2 2 3 2 2
+--R (2a b c d - 2b c )x + (4a c d - 4a b c )x
+--R *
+--R +--------+
+--R | 2
+--R \|b x + a
+--R +
+--R 2 2 3 2 2 +-+
+--R ((- 4a b c d + 4b c )x + (- 4a c d + 4a b c )x)\|a
+--R +
+--R +--------------+
+--R 2 4 2 2 2 | 2
+--R ((a b d - 2b c)x + (2a d - 5a b c)x - 2a c)\|- a c d + b c
+--R /
+--R +--------+
+--R 2 +-+ | 2 4 2
+--R (2d x + 2c)\|a \|b x + a - b d x + (- 2a d - b c)x - 2a c
+--R +
+--R +--------------+ +--------+
+--R 3 | 2 | 2
+--R (- 2b d x - 4a d x)\|- a c d + b c \|b x + a
+--R +
+--R +--------------+
+--R 3 | 2 +-+
+--R (4b d x + 4a d x)\|- a c d + b c \|a
+--R /
+--R +--------------+ +--------+
+--R 2 2 2 2 3 | 2 +-+ | 2
+--R ((8a c d - 8b c d)x + 8a c d - 8b c )\|- a c d + b c \|a \|b x + a
+--R +
+--R 2 2 2 4 2 2 2 2 3 2
+--R (- 4a b c d + 4b c d)x + (- 8a c d + 4a b c d + 4b c )x
+--R +
+--R 2 2 3
+--R - 8a c d + 8a b c
+--R *
+--R +--------------+
+--R | 2
+--R \|- a c d + b c
+--R ,
+--R
+--R +--------+
+--R 2 2 2 +-+ | 2
+--R ((2a d - 4b c d)x + 2a c d - 4b c )\|a \|b x + a
+--R +
+--R 2 2 4 2 2 2 2 2 2
+--R (- a b d + 2b c d)x + (- 2a d + 3a b c d + 2b c )x - 2a c d
+--R +
+--R 2
+--R 4a b c
+--R *
+--R +--------+
+--R 2 | 2 2 +-+
+--R ((a d - b c)x + a c)\|b x + a + (- a d x - a c)\|a
+--R atan(-------------------------------------------------------)
+--R +------------+
+--R 3 | 2
+--R b x \|a c d - b c
+--R +
+--R +--------+
+--R 2 2 2 +-+ | 2
+--R ((2a d - 4b c d)x + 2a c d - 4b c )\|a \|b x + a
+--R +
+--R 2 2 4 2 2 2 2 2 2
+--R (- a b d + 2b c d)x + (- 2a d + 3a b c d + 2b c )x - 2a c d
+--R +
+--R 2
+--R 4a b c
+--R *
+--R +------------+
+--R +-+ | 2
+--R \|a \|a c d - b c
+--R atan(-------------------)
+--R (a d - b c)x
+--R +
+--R +------------+ +--------+
+--R 3 | 2 | 2
+--R (- b d x - 2a d x)\|a c d - b c \|b x + a
+--R +
+--R +------------+
+--R 3 +-+ | 2
+--R (2b d x + 2a d x)\|a \|a c d - b c
+--R /
+--R +------------+ +--------+
+--R 2 2 2 2 3 +-+ | 2 | 2
+--R ((4a c d - 4b c d)x + 4a c d - 4b c )\|a \|a c d - b c \|b x + a
+--R +
+--R 2 2 2 4 2 2 2 2 3 2
+--R (- 2a b c d + 2b c d)x + (- 4a c d + 2a b c d + 2b c )x
+--R +
+--R 2 2 3
+--R - 4a c d + 4a b c
+--R *
+--R +------------+
+--R | 2
+--R \|a c d - b c
+--R ]
+--R Type: Union(List(Expression(Integer)),...)
+--E 450
+
+--S 451 of 994
+m0a:=a0.1-r0
+--R
+--R
+--R (4)
+--R +-----------+ +-+
+--R (a d - 2b c)\|- a d + b c \|c
+--R *
+--R log
+--R +--------------+
+--R 2 | 2 +-+
+--R ((- 2a d + 4b c)x + 2a c)\|- a c d + b c \|a
+--R +
+--R 2 2 3 2 2
+--R (2a b c d - 2b c )x + (4a c d - 4a b c )x
+--R *
+--R +--------+
+--R | 2
+--R \|b x + a
+--R +
+--R 2 2 3 2 2 +-+
+--R ((- 4a b c d + 4b c )x + (- 4a c d + 4a b c )x)\|a
+--R +
+--R +--------------+
+--R 2 4 2 2 2 | 2
+--R ((a b d - 2b c)x + (2a d - 5a b c)x - 2a c)\|- a c d + b c
+--R /
+--R +--------+
+--R 2 +-+ | 2 4 2
+--R (2d x + 2c)\|a \|b x + a - b d x + (- 2a d - b c)x - 2a c
+--R +
+--R +--------------+ +-----------+
+--R | 2 x\|- a d + b c
+--R (- 2a d + 4b c)\|- a c d + b c atanh(---------------)
+--R +--------+
+--R +-+ | 2
+--R \|c \|b x + a
+--R /
+--R +--------------+
+--R 2 | 2 +-----------+ +-+
+--R (4a c d - 4b c )\|- a c d + b c \|- a d + b c \|c
+--R Type: Expression(Integer)
+--E 451
+
+--S 452 of 994
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 452
+
+--S 453 of 994
+m0b:=a0.2-r0
+--R
+--R
+--R (6)
+--R +------------+ +-----------+
+--R | 2 x\|- a d + b c
+--R (- a d + 2b c)\|a c d - b c atanh(---------------)
+--R +--------+
+--R +-+ | 2
+--R \|c \|b x + a
+--R +
+--R +-----------+ +-+
+--R (a d - 2b c)\|- a d + b c \|c
+--R *
+--R +--------+
+--R 2 | 2 2 +-+
+--R ((a d - b c)x + a c)\|b x + a + (- a d x - a c)\|a
+--R atan(-------------------------------------------------------)
+--R +------------+
+--R 3 | 2
+--R b x \|a c d - b c
+--R +
+--R +------------+
+--R +-+ | 2
+--R +-----------+ +-+ \|a \|a c d - b c
+--R (a d - 2b c)\|- a d + b c \|c atan(-------------------)
+--R (a d - b c)x
+--R /
+--R +------------+
+--R 2 +-----------+ +-+ | 2
+--R (2a c d - 2b c )\|- a d + b c \|c \|a c d - b c
+--R Type: Expression(Integer)
+--E 453
+
+--S 454 of 994
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 454
+
+)clear all
+
+--S 455 of 994
+t0:=1/((a+b*x^2)^(1/2)*(c+d*x^2)^3)
+--R
+--R
+--R 1
+--R (1) ------------------------------------------
+--R +--------+
+--R 3 6 2 4 2 2 3 | 2
+--R (d x + 3c d x + 3c d x + c )\|b x + a
+--R Type: Expression(Integer)
+--E 455
+
+--S 456 of 994
+r0:=1/8*(8*b^2*c^2-8*a*b*c*d+3*a^2*d^2)*atanh(x*sqrt(b*c-a*d)/(sqrt(c)*_
+ sqrt(a+b*x^2)))/(c^(5/2)*(b*c-a*d)^(5/2))-1/4*d*x*sqrt(a+b*x^2)/_
+ (c*(b*c-a*d)*(c+d*x^2)^2)-3/8*d*(2*b*c-a*d)*x*sqrt(a+b*x^2)/_
+ (c^2*(b*c-a*d)^2*(c+d*x^2))
+--R
+--R
+--R (2)
+--R 2 4 3 2 2 2 4 2 3 2 2 2 3 2
+--R (3a d - 8a b c d + 8b c d )x + (6a c d - 16a b c d + 16b c d)x
+--R +
+--R 2 2 2 3 2 4
+--R 3a c d - 8a b c d + 8b c
+--R *
+--R +-----------+
+--R x\|- a d + b c
+--R atanh(---------------)
+--R +--------+
+--R +-+ | 2
+--R \|c \|b x + a
+--R +
+--R +--------+
+--R 3 2 3 2 2 +-----------+ +-+ | 2
+--R ((3a d - 6b c d )x + (5a c d - 8b c d)x)\|- a d + b c \|c \|b x + a
+--R /
+--R 2 2 4 3 3 2 4 2 4
+--R (8a c d - 16a b c d + 8b c d )x
+--R +
+--R 2 3 3 4 2 2 5 2 2 4 2 5 2 6
+--R (16a c d - 32a b c d + 16b c d)x + 8a c d - 16a b c d + 8b c
+--R *
+--R +-----------+ +-+
+--R \|- a d + b c \|c
+--R Type: Expression(Integer)
+--E 456
+
+--S 457 of 994
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R 2 4 2 3 3 2 2 6
+--R (12a b d - 32a b c d + 32b c d )x
+--R +
+--R 3 4 2 3 3 3 4
+--R (24a d - 40a b c d + 64b c d)x
+--R +
+--R 3 3 2 2 2 2 3 3 4 2 3 2 2
+--R (48a c d - 116a b c d + 96a b c d + 32b c )x + 24a c d
+--R +
+--R 2 3 2 4
+--R - 64a b c d + 64a b c
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|a \|b x + a
+--R +
+--R 2 2 4 3 3 4 2 2 8
+--R (- 3a b d + 8a b c d - 8b c d )x
+--R +
+--R 3 4 2 2 3 3 2 2 4 3 6
+--R (- 24a b d + 58a b c d - 48a b c d - 16b c d)x
+--R +
+--R 4 4 3 3 2 2 2 2 3 3 4 4 4
+--R (- 24a d + 16a b c d + 61a b c d - 120a b c d - 8b c )x
+--R +
+--R 4 3 3 2 2 2 2 3 3 4 2 4 2 2
+--R (- 48a c d + 104a b c d - 64a b c d - 64a b c )x - 24a c d
+--R +
+--R 3 3 2 2 4
+--R 64a b c d - 64a b c
+--R *
+--R log
+--R +--------------+
+--R 2 | 2 +-+
+--R ((- 2a d + 4b c)x + 2a c)\|- a c d + b c \|a
+--R +
+--R 2 2 3 2 2
+--R (2a b c d - 2b c )x + (4a c d - 4a b c )x
+--R *
+--R +--------+
+--R | 2
+--R \|b x + a
+--R +
+--R 2 2 3 2 2 +-+
+--R ((- 4a b c d + 4b c )x + (- 4a c d + 4a b c )x)\|a
+--R +
+--R +--------------+
+--R 2 4 2 2 2 | 2
+--R ((a b d - 2b c)x + (2a d - 5a b c)x - 2a c)\|- a c d + b c
+--R /
+--R +--------+
+--R 2 +-+ | 2 4 2
+--R (2d x + 2c)\|a \|b x + a - b d x + (- 2a d - b c)x - 2a c
+--R +
+--R 2 3 3 2 7 2 3 2 2 3 2 5
+--R (- 6a b d + 12b c d )x + (- 48a b d + 86a b c d + 16b c d)x
+--R +
+--R 3 3 2 2 2 2 3 3 2 2 2
+--R (- 48a d + 16a b c d + 128a b c d)x + (- 80a c d + 128a b c d)x
+--R *
+--R +--------------+ +--------+
+--R | 2 | 2
+--R \|- a c d + b c \|b x + a
+--R +
+--R 2 3 3 2 7 2 3 2 2 3 2 5
+--R (24a b d - 48b c d )x + (72a b d - 104a b c d - 64b c d)x
+--R +
+--R 3 3 2 2 2 2 3 3 2 2 2
+--R (48a d + 24a b c d - 192a b c d)x + (80a c d - 128a b c d)x
+--R *
+--R +--------------+
+--R | 2 +-+
+--R \|- a c d + b c \|a
+--R /
+--R 2 2 4 2 3 3 3 4 2 6
+--R (64a b c d - 128a b c d + 64b c d )x
+--R +
+--R 3 2 4 2 3 3 2 4 2 3 5 4
+--R (128a c d - 128a b c d - 128a b c d + 128b c d)x
+--R +
+--R 3 3 3 2 4 2 2 5 3 6 2 3 4 2
+--R (256a c d - 448a b c d + 128a b c d + 64b c )x + 128a c d
+--R +
+--R 2 5 2 6
+--R - 256a b c d + 128a b c
+--R *
+--R +--------------+ +--------+
+--R | 2 +-+ | 2
+--R \|- a c d + b c \|a \|b x + a
+--R +
+--R 2 2 2 4 3 3 3 4 4 2 8
+--R (- 16a b c d + 32a b c d - 16b c d )x
+--R +
+--R 3 2 4 2 2 3 3 3 4 2 4 5 6
+--R (- 128a b c d + 224a b c d - 64a b c d - 32b c d)x
+--R +
+--R 4 2 4 2 2 4 2 3 5 4 6 4
+--R (- 128a c d + 368a b c d - 224a b c d - 16b c )x
+--R +
+--R 4 3 3 3 4 2 3 6 2 4 4 2 3 5
+--R (- 256a c d + 384a b c d - 128a b c )x - 128a c d + 256a b c d
+--R +
+--R 2 2 6
+--R - 128a b c
+--R *
+--R +--------------+
+--R | 2
+--R \|- a c d + b c
+--R ,
+--R
+--R 2 4 2 3 3 2 2 6
+--R (12a b d - 32a b c d + 32b c d )x
+--R +
+--R 3 4 2 3 3 3 4
+--R (24a d - 40a b c d + 64b c d)x
+--R +
+--R 3 3 2 2 2 2 3 3 4 2 3 2 2
+--R (48a c d - 116a b c d + 96a b c d + 32b c )x + 24a c d
+--R +
+--R 2 3 2 4
+--R - 64a b c d + 64a b c
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|a \|b x + a
+--R +
+--R 2 2 4 3 3 4 2 2 8
+--R (- 3a b d + 8a b c d - 8b c d )x
+--R +
+--R 3 4 2 2 3 3 2 2 4 3 6
+--R (- 24a b d + 58a b c d - 48a b c d - 16b c d)x
+--R +
+--R 4 4 3 3 2 2 2 2 3 3 4 4 4
+--R (- 24a d + 16a b c d + 61a b c d - 120a b c d - 8b c )x
+--R +
+--R 4 3 3 2 2 2 2 3 3 4 2 4 2 2
+--R (- 48a c d + 104a b c d - 64a b c d - 64a b c )x - 24a c d
+--R +
+--R 3 3 2 2 4
+--R 64a b c d - 64a b c
+--R *
+--R +--------+
+--R 2 | 2 2 +-+
+--R ((a d - b c)x + a c)\|b x + a + (- a d x - a c)\|a
+--R atan(-------------------------------------------------------)
+--R +------------+
+--R 3 | 2
+--R b x \|a c d - b c
+--R +
+--R 2 4 2 3 3 2 2 6
+--R (12a b d - 32a b c d + 32b c d )x
+--R +
+--R 3 4 2 3 3 3 4
+--R (24a d - 40a b c d + 64b c d)x
+--R +
+--R 3 3 2 2 2 2 3 3 4 2 3 2 2
+--R (48a c d - 116a b c d + 96a b c d + 32b c )x + 24a c d
+--R +
+--R 2 3 2 4
+--R - 64a b c d + 64a b c
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|a \|b x + a
+--R +
+--R 2 2 4 3 3 4 2 2 8
+--R (- 3a b d + 8a b c d - 8b c d )x
+--R +
+--R 3 4 2 2 3 3 2 2 4 3 6
+--R (- 24a b d + 58a b c d - 48a b c d - 16b c d)x
+--R +
+--R 4 4 3 3 2 2 2 2 3 3 4 4 4
+--R (- 24a d + 16a b c d + 61a b c d - 120a b c d - 8b c )x
+--R +
+--R 4 3 3 2 2 2 2 3 3 4 2 4 2 2
+--R (- 48a c d + 104a b c d - 64a b c d - 64a b c )x - 24a c d
+--R +
+--R 3 3 2 2 4
+--R 64a b c d - 64a b c
+--R *
+--R +------------+
+--R +-+ | 2
+--R \|a \|a c d - b c
+--R atan(-------------------)
+--R (a d - b c)x
+--R +
+--R 2 3 3 2 7 2 3 2 2 3 2 5
+--R (- 3a b d + 6b c d )x + (- 24a b d + 43a b c d + 8b c d)x
+--R +
+--R 3 3 2 2 2 2 3 3 2 2 2
+--R (- 24a d + 8a b c d + 64a b c d)x + (- 40a c d + 64a b c d)x
+--R *
+--R +------------+ +--------+
+--R | 2 | 2
+--R \|a c d - b c \|b x + a
+--R +
+--R 2 3 3 2 7 2 3 2 2 3 2 5
+--R (12a b d - 24b c d )x + (36a b d - 52a b c d - 32b c d)x
+--R +
+--R 3 3 2 2 2 2 3 3 2 2 2
+--R (24a d + 12a b c d - 96a b c d)x + (40a c d - 64a b c d)x
+--R *
+--R +------------+
+--R +-+ | 2
+--R \|a \|a c d - b c
+--R /
+--R 2 2 4 2 3 3 3 4 2 6
+--R (32a b c d - 64a b c d + 32b c d )x
+--R +
+--R 3 2 4 2 3 3 2 4 2 3 5 4
+--R (64a c d - 64a b c d - 64a b c d + 64b c d)x
+--R +
+--R 3 3 3 2 4 2 2 5 3 6 2 3 4 2
+--R (128a c d - 224a b c d + 64a b c d + 32b c )x + 64a c d
+--R +
+--R 2 5 2 6
+--R - 128a b c d + 64a b c
+--R *
+--R +------------+ +--------+
+--R +-+ | 2 | 2
+--R \|a \|a c d - b c \|b x + a
+--R +
+--R 2 2 2 4 3 3 3 4 4 2 8
+--R (- 8a b c d + 16a b c d - 8b c d )x
+--R +
+--R 3 2 4 2 2 3 3 3 4 2 4 5 6
+--R (- 64a b c d + 112a b c d - 32a b c d - 16b c d)x
+--R +
+--R 4 2 4 2 2 4 2 3 5 4 6 4
+--R (- 64a c d + 184a b c d - 112a b c d - 8b c )x
+--R +
+--R 4 3 3 3 4 2 3 6 2 4 4 2 3 5
+--R (- 128a c d + 192a b c d - 64a b c )x - 64a c d + 128a b c d
+--R +
+--R 2 2 6
+--R - 64a b c
+--R *
+--R +------------+
+--R | 2
+--R \|a c d - b c
+--R ]
+--R Type: Union(List(Expression(Integer)),...)
+--E 457
+
+--S 458 of 994
+m0a:=a0.1-r0
+--R
+--R
+--R (4)
+--R 2 2 2 2 +-----------+ +-+
+--R (3a d - 8a b c d + 8b c )\|- a d + b c \|c
+--R *
+--R log
+--R +--------------+
+--R 2 | 2 +-+
+--R ((- 2a d + 4b c)x + 2a c)\|- a c d + b c \|a
+--R +
+--R 2 2 3 2 2
+--R (2a b c d - 2b c )x + (4a c d - 4a b c )x
+--R *
+--R +--------+
+--R | 2
+--R \|b x + a
+--R +
+--R 2 2 3 2 2 +-+
+--R ((- 4a b c d + 4b c )x + (- 4a c d + 4a b c )x)\|a
+--R +
+--R +--------------+
+--R 2 4 2 2 2 | 2
+--R ((a b d - 2b c)x + (2a d - 5a b c)x - 2a c)\|- a c d + b c
+--R /
+--R +--------+
+--R 2 +-+ | 2 4 2
+--R (2d x + 2c)\|a \|b x + a - b d x + (- 2a d - b c)x - 2a c
+--R +
+--R +--------------+ +-----------+
+--R 2 2 2 2 | 2 x\|- a d + b c
+--R (- 6a d + 16a b c d - 16b c )\|- a c d + b c atanh(---------------)
+--R +--------+
+--R +-+ | 2
+--R \|c \|b x + a
+--R /
+--R +--------------+
+--R 2 2 2 3 2 4 | 2 +-----------+ +-+
+--R (16a c d - 32a b c d + 16b c )\|- a c d + b c \|- a d + b c \|c
+--R Type: Expression(Integer)
+--E 458
+
+--S 459 of 994
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 459
+
+--S 460 of 994
+m0b:=a0.2-r0
+--R
+--R
+--R (6)
+--R +------------+ +-----------+
+--R 2 2 2 2 | 2 x\|- a d + b c
+--R (- 3a d + 8a b c d - 8b c )\|a c d - b c atanh(---------------)
+--R +--------+
+--R +-+ | 2
+--R \|c \|b x + a
+--R +
+--R 2 2 2 2 +-----------+ +-+
+--R (3a d - 8a b c d + 8b c )\|- a d + b c \|c
+--R *
+--R +--------+
+--R 2 | 2 2 +-+
+--R ((a d - b c)x + a c)\|b x + a + (- a d x - a c)\|a
+--R atan(-------------------------------------------------------)
+--R +------------+
+--R 3 | 2
+--R b x \|a c d - b c
+--R +
+--R +------------+
+--R +-+ | 2
+--R 2 2 2 2 +-----------+ +-+ \|a \|a c d - b c
+--R (3a d - 8a b c d + 8b c )\|- a d + b c \|c atan(-------------------)
+--R (a d - b c)x
+--R /
+--R +------------+
+--R 2 2 2 3 2 4 +-----------+ +-+ | 2
+--R (8a c d - 16a b c d + 8b c )\|- a d + b c \|c \|a c d - b c
+--R Type: Expression(Integer)
+--E 460
+
+--S 461 of 994
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 461
+
+)clear all
+
+--S 462 of 994
+t0:=(c+d*x^2)^4/(a+b*x^2)^(3/2)
+--R
+--R
+--R 4 8 3 6 2 2 4 3 2 4
+--R d x + 4c d x + 6c d x + 4c d x + c
+--R (1) ---------------------------------------
+--R +--------+
+--R 2 | 2
+--R (b x + a)\|b x + a
+--R Type: Expression(Integer)
+--E 462
+
+--S 463 of 994
+r0:=1/16*d*(64*b^3*c^3-144*a*b^2*c^2*d+120*a^2*b*c*d^2-35*a^3*d^3)*_
+ atanh(x*sqrt(b)/sqrt(a+b*x^2))/b^(9/2)+(b*c-a*d)*x*(c+d*x^2)^3/_
+ (a*b*sqrt(a+b*x^2))-1/48*d*(96*b^3*c^3-352*a*b^2*c^2*d+346*_
+ a^2*b*c*d^2-105*a^3*d^3)*x*sqrt(a+b*x^2)/(a*b^4)-1/6*d*(6*b*c-_
+ 7*a*d)*x*(c+d*x^2)^2*sqrt(a+b*x^2)/(a*b^2)+1/24*d^2*x*(a*c*_
+ (12*b*c-7*a*d)-(24*b^2*c^2-64*a*b*c*d+35*a^2*d^2)*x^2)*_
+ sqrt(a+b*x^2)/(a*b^3)
+--R
+--R
+--R (2)
+--R +--------+
+--R 4 4 3 3 2 2 2 2 3 3 | 2
+--R (- 105a d + 360a b c d - 432a b c d + 192a b c d)\|b x + a
+--R *
+--R +-+
+--R x\|b
+--R atanh(-----------)
+--R +--------+
+--R | 2
+--R \|b x + a
+--R +
+--R 3 4 7 2 2 4 3 3 5
+--R 8a b d x + (- 14a b d + 48a b c d )x
+--R +
+--R 3 4 2 2 3 3 2 2 3
+--R (35a b d - 120a b c d + 144a b c d )x
+--R +
+--R 4 4 3 3 2 2 2 2 3 3 4 4
+--R (105a d - 360a b c d + 432a b c d - 192a b c d + 48b c )x
+--R *
+--R +-+
+--R \|b
+--R /
+--R +--------+
+--R 4 +-+ | 2
+--R 48a b \|b \|b x + a
+--R Type: Expression(Integer)
+--E 463
+
+--S 464 of 994
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R 4 3 4 3 4 3 2 5 2 2 6 3 6
+--R (735a b d - 2520a b c d + 3024a b c d - 1344a b c d)x
+--R +
+--R 5 2 4 4 3 3 3 4 2 2 2 5 3 4
+--R (5880a b d - 20160a b c d + 24192a b c d - 10752a b c d)x
+--R +
+--R 6 4 5 2 3 4 3 2 2 3 4 3 2
+--R (11760a b d - 40320a b c d + 48384a b c d - 21504a b c d)x
+--R +
+--R 7 4 6 3 5 2 2 2 4 3 3
+--R 6720a d - 23040a b c d + 27648a b c d - 12288a b c d
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|a \|b x + a
+--R +
+--R 4 4 4 3 5 3 2 6 2 2 7 3 8
+--R (- 105a b d + 360a b c d - 432a b c d + 192a b c d)x
+--R +
+--R 5 3 4 4 4 3 3 5 2 2 2 6 3 6
+--R (- 2625a b d + 9000a b c d - 10800a b c d + 4800a b c d)x
+--R +
+--R 6 2 4 5 3 3 4 4 2 2 3 5 3 4
+--R (- 10920a b d + 37440a b c d - 44928a b c d + 19968a b c d)x
+--R +
+--R 7 4 6 2 3 5 3 2 2 4 4 3 2
+--R (- 15120a b d + 51840a b c d - 62208a b c d + 27648a b c d)x
+--R +
+--R 8 4 7 3 6 2 2 2 5 3 3
+--R - 6720a d + 23040a b c d - 27648a b c d + 12288a b c d
+--R *
+--R +--------+
+--R +-+ +-+ | 2 2 +-+ +-+
+--R (\|a \|b + b x)\|b x + a + (- b x - a)\|b - b x\|a
+--R log(--------------------------------------------------------)
+--R +--------+
+--R +-+ | 2
+--R \|a \|b x + a - a
+--R +
+--R 6 4 13 2 5 4 6 3 11
+--R - 8a b d x + (- 178a b d - 48a b c d )x
+--R +
+--R 3 4 4 2 5 3 6 2 2 9
+--R (- 339a b d - 1032a b c d - 144a b c d )x
+--R +
+--R 4 3 4 3 4 3 2 5 2 2 6 3 7 4 7
+--R (- 337a b d - 600a b c d - 3888a b c d + 192a b c d - 48b c )x
+--R +
+--R 5 2 4 4 3 3 3 4 2 2 2 5 3
+--R - 4424a b d + 15168a b c d - 21888a b c d + 4608a b c d
+--R +
+--R 6 4
+--R - 1152a b c
+--R *
+--R 5
+--R x
+--R +
+--R 6 4 5 2 3 4 3 2 2 3 4 3
+--R - 10640a b d + 36480a b c d - 43776a b c d + 15360a b c d
+--R +
+--R 2 5 4
+--R - 3840a b c
+--R *
+--R 3
+--R x
+--R +
+--R 7 4 6 3 5 2 2 2 4 3 3
+--R - 6720a d + 23040a b c d - 27648a b c d + 12288a b c d
+--R +
+--R 3 4 4
+--R - 3072a b c
+--R *
+--R x
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|b \|b x + a
+--R +
+--R 6 4 13 2 5 4 6 3 11
+--R 56a b d x + (350a b d + 336a b c d )x
+--R +
+--R 3 4 4 2 5 3 6 2 2 9
+--R (357a b d + 1848a b c d + 1008a b c d )x
+--R +
+--R 4 3 4 3 4 3 2 5 2 2 6 3
+--R 1639a b d - 3864a b c d + 11088a b c d - 1344a b c d
+--R +
+--R 7 4
+--R 336b c
+--R *
+--R 7
+--R x
+--R +
+--R 5 2 4 4 3 3 3 4 2 2 2 5 3
+--R 8904a b d - 30528a b c d + 40320a b c d - 10752a b c d
+--R +
+--R 6 4
+--R 2688a b c
+--R *
+--R 5
+--R x
+--R +
+--R 6 4 5 2 3 4 3 2 2 3 4 3
+--R 14000a b d - 48000a b c d + 57600a b c d - 21504a b c d
+--R +
+--R 2 5 4
+--R 5376a b c
+--R *
+--R 3
+--R x
+--R +
+--R 7 4 6 3 5 2 2 2 4 3 3
+--R 6720a d - 23040a b c d + 27648a b c d - 12288a b c d
+--R +
+--R 3 4 4
+--R 3072a b c
+--R *
+--R x
+--R *
+--R +-+ +-+
+--R \|a \|b
+--R /
+--R +--------+
+--R 7 6 2 6 4 3 5 2 4 4 +-+ +-+ | 2
+--R (336a b x + 2688a b x + 5376a b x + 3072a b )\|a \|b \|b x + a
+--R +
+--R 8 8 2 7 6 3 6 4 4 5 2 5 4 +-+
+--R (- 48a b x - 1200a b x - 4992a b x - 6912a b x - 3072a b )\|b
+--R ,
+--R
+--R 4 3 4 3 4 3 2 5 2 2 6 3 6
+--R (- 1470a b d + 5040a b c d - 6048a b c d + 2688a b c d)x
+--R +
+--R 5 2 4 4 3 3 3 4 2 2
+--R - 11760a b d + 40320a b c d - 48384a b c d
+--R +
+--R 2 5 3
+--R 21504a b c d
+--R *
+--R 4
+--R x
+--R +
+--R 6 4 5 2 3 4 3 2 2
+--R - 23520a b d + 80640a b c d - 96768a b c d
+--R +
+--R 3 4 3
+--R 43008a b c d
+--R *
+--R 2
+--R x
+--R +
+--R 7 4 6 3 5 2 2 2 4 3 3
+--R - 13440a d + 46080a b c d - 55296a b c d + 24576a b c d
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|a \|b x + a
+--R +
+--R 4 4 4 3 5 3 2 6 2 2 7 3 8
+--R (210a b d - 720a b c d + 864a b c d - 384a b c d)x
+--R +
+--R 5 3 4 4 4 3 3 5 2 2 2 6 3 6
+--R (5250a b d - 18000a b c d + 21600a b c d - 9600a b c d)x
+--R +
+--R 6 2 4 5 3 3 4 4 2 2 3 5 3 4
+--R (21840a b d - 74880a b c d + 89856a b c d - 39936a b c d)x
+--R +
+--R 7 4 6 2 3 5 3 2 2 4 4 3 2
+--R (30240a b d - 103680a b c d + 124416a b c d - 55296a b c d)x
+--R +
+--R 8 4 7 3 6 2 2 2 5 3 3
+--R 13440a d - 46080a b c d + 55296a b c d - 24576a b c d
+--R *
+--R +--------+
+--R +---+ | 2 +---+ +-+
+--R \|- b \|b x + a - \|- b \|a
+--R atan(------------------------------)
+--R b x
+--R +
+--R 6 4 13 2 5 4 6 3 11
+--R - 8a b d x + (- 178a b d - 48a b c d )x
+--R +
+--R 3 4 4 2 5 3 6 2 2 9
+--R (- 339a b d - 1032a b c d - 144a b c d )x
+--R +
+--R 4 3 4 3 4 3 2 5 2 2 6 3 7 4 7
+--R (- 337a b d - 600a b c d - 3888a b c d + 192a b c d - 48b c )x
+--R +
+--R 5 2 4 4 3 3 3 4 2 2 2 5 3
+--R - 4424a b d + 15168a b c d - 21888a b c d + 4608a b c d
+--R +
+--R 6 4
+--R - 1152a b c
+--R *
+--R 5
+--R x
+--R +
+--R 6 4 5 2 3 4 3 2 2 3 4 3
+--R - 10640a b d + 36480a b c d - 43776a b c d + 15360a b c d
+--R +
+--R 2 5 4
+--R - 3840a b c
+--R *
+--R 3
+--R x
+--R +
+--R 7 4 6 3 5 2 2 2 4 3 3
+--R - 6720a d + 23040a b c d - 27648a b c d + 12288a b c d
+--R +
+--R 3 4 4
+--R - 3072a b c
+--R *
+--R x
+--R *
+--R +--------+
+--R +---+ | 2
+--R \|- b \|b x + a
+--R +
+--R 6 4 13 2 5 4 6 3 11
+--R 56a b d x + (350a b d + 336a b c d )x
+--R +
+--R 3 4 4 2 5 3 6 2 2 9
+--R (357a b d + 1848a b c d + 1008a b c d )x
+--R +
+--R 4 3 4 3 4 3 2 5 2 2 6 3
+--R 1639a b d - 3864a b c d + 11088a b c d - 1344a b c d
+--R +
+--R 7 4
+--R 336b c
+--R *
+--R 7
+--R x
+--R +
+--R 5 2 4 4 3 3 3 4 2 2 2 5 3
+--R 8904a b d - 30528a b c d + 40320a b c d - 10752a b c d
+--R +
+--R 6 4
+--R 2688a b c
+--R *
+--R 5
+--R x
+--R +
+--R 6 4 5 2 3 4 3 2 2 3 4 3
+--R 14000a b d - 48000a b c d + 57600a b c d - 21504a b c d
+--R +
+--R 2 5 4
+--R 5376a b c
+--R *
+--R 3
+--R x
+--R +
+--R 7 4 6 3 5 2 2 2 4 3 3
+--R 6720a d - 23040a b c d + 27648a b c d - 12288a b c d
+--R +
+--R 3 4 4
+--R 3072a b c
+--R *
+--R x
+--R *
+--R +---+ +-+
+--R \|- b \|a
+--R /
+--R +--------+
+--R 7 6 2 6 4 3 5 2 4 4 +---+ +-+ | 2
+--R (336a b x + 2688a b x + 5376a b x + 3072a b )\|- b \|a \|b x + a
+--R +
+--R 8 8 2 7 6 3 6 4 4 5 2 5 4 +---+
+--R (- 48a b x - 1200a b x - 4992a b x - 6912a b x - 3072a b )\|- b
+--R ]
+--R Type: Union(List(Expression(Integer)),...)
+--E 464
+
+--S 465 of 994
+m0a:=a0.1-r0
+--R
+--R
+--R (4)
+--R 3 4 2 3 2 2 2 3 3
+--R (35a d - 120a b c d + 144a b c d - 64b c d)
+--R *
+--R +--------+
+--R +-+ +-+ | 2 2 +-+ +-+
+--R (\|a \|b + b x)\|b x + a + (- b x - a)\|b - b x\|a
+--R log(--------------------------------------------------------)
+--R +--------+
+--R +-+ | 2
+--R \|a \|b x + a - a
+--R +
+--R +-+
+--R 3 4 2 3 2 2 2 3 3 x\|b
+--R (35a d - 120a b c d + 144a b c d - 64b c d)atanh(-----------)
+--R +--------+
+--R | 2
+--R \|b x + a
+--R /
+--R 4 +-+
+--R 16b \|b
+--R Type: Expression(Integer)
+--E 465
+
+--S 466 of 994
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 466
+
+--S 467 of 994
+m0b:=a0.2-r0
+--R
+--R
+--R (6)
+--R +-+
+--R 3 4 2 3 2 2 2 3 3 +---+ x\|b
+--R (35a d - 120a b c d + 144a b c d - 64b c d)\|- b atanh(-----------)
+--R +--------+
+--R | 2
+--R \|b x + a
+--R +
+--R 3 4 2 3 2 2 2 3 3 +-+
+--R (- 70a d + 240a b c d - 288a b c d + 128b c d)\|b
+--R *
+--R +--------+
+--R +---+ | 2 +---+ +-+
+--R \|- b \|b x + a - \|- b \|a
+--R atan(------------------------------)
+--R b x
+--R /
+--R 4 +---+ +-+
+--R 16b \|- b \|b
+--R Type: Expression(Integer)
+--E 467
+
+--S 468 of 994
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 468
+
+)clear all
+
+--S 469 of 994
+t0:=(c+d*x^2)^3/(a+b*x^2)^(3/2)
+--R
+--R
+--R 3 6 2 4 2 2 3
+--R d x + 3c d x + 3c d x + c
+--R (1) -----------------------------
+--R +--------+
+--R 2 | 2
+--R (b x + a)\|b x + a
+--R Type: Expression(Integer)
+--E 469
+
+--S 470 of 994
+r0:=3/8*d*(8*b^2*c^2-12*a*b*c*d+5*a^2*d^2)*atanh(x*sqrt(b)/_
+ sqrt(a+b*x^2))/b^(7/2)+(b*c-a*d)*x*(c+d*x^2)^2/(a*b*_
+ sqrt(a+b*x^2))-1/8*d*(8*b*c-5*a*d)*(2*b*c-3*a*d)*x*_
+ sqrt(a+b*x^2)/(a*b^3)+1/4*d^2*x*(a*c-(4*b*c-5*a*d)*x^2)*_
+ sqrt(a+b*x^2)/(a*b^2)
+--R
+--R
+--R (2)
+--R +--------+ +-+
+--R 3 3 2 2 2 2 | 2 x\|b
+--R (15a d - 36a b c d + 24a b c d)\|b x + a atanh(-----------)
+--R +--------+
+--R | 2
+--R \|b x + a
+--R +
+--R 2 3 5 2 3 2 2 3
+--R 2a b d x + (- 5a b d + 12a b c d )x
+--R +
+--R 3 3 2 2 2 2 3 3
+--R (- 15a d + 36a b c d - 24a b c d + 8b c )x
+--R *
+--R +-+
+--R \|b
+--R /
+--R +--------+
+--R 3 +-+ | 2
+--R 8a b \|b \|b x + a
+--R Type: Expression(Integer)
+--E 470
+
+--S 471 of 994
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R 3 2 3 2 3 2 4 2 4
+--R (75a b d - 180a b c d + 120a b c d)x
+--R +
+--R 4 3 3 2 2 2 3 2 2 5 3
+--R (300a b d - 720a b c d + 480a b c d)x + 240a d
+--R +
+--R 4 2 3 2 2
+--R - 576a b c d + 384a b c d
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|a \|b x + a
+--R +
+--R 3 3 3 2 4 2 5 2 6
+--R (- 15a b d + 36a b c d - 24a b c d)x
+--R +
+--R 4 2 3 3 3 2 2 4 2 4
+--R (- 195a b d + 468a b c d - 312a b c d)x
+--R +
+--R 5 3 4 2 2 3 3 2 2 6 3 5 2
+--R (- 420a b d + 1008a b c d - 672a b c d)x - 240a d + 576a b c d
+--R +
+--R 4 2 2
+--R - 384a b c d
+--R *
+--R +--------+
+--R +-+ +-+ | 2 2 +-+ +-+
+--R (\|a \|b - b x)\|b x + a + (- b x - a)\|b + b x\|a
+--R log(--------------------------------------------------------)
+--R +--------+
+--R +-+ | 2
+--R \|a \|b x + a - a
+--R +
+--R 4 3 9 2 3 3 4 2 7
+--R - 2a b d x + (- 19a b d - 12a b c d )x
+--R +
+--R 3 2 3 2 3 2 4 2 5 3 5
+--R (43a b d - 180a b c d + 24a b c d - 8b c )x
+--R +
+--R 4 3 3 2 2 2 3 2 4 3 3
+--R (260a b d - 624a b c d + 288a b c d - 96a b c )x
+--R +
+--R 5 3 4 2 3 2 2 2 3 3
+--R (240a d - 576a b c d + 384a b c d - 128a b c )x
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|b \|b x + a
+--R +
+--R 4 3 9 2 3 3 4 2 7
+--R 10a b d x + (15a b d + 60a b c d )x
+--R +
+--R 3 2 3 2 3 2 4 2 5 3 5
+--R (- 143a b d + 420a b c d - 120a b c d + 40b c )x
+--R +
+--R 4 3 3 2 2 2 3 2 4 3 3
+--R (- 380a b d + 912a b c d - 480a b c d + 160a b c )x
+--R +
+--R 5 3 4 2 3 2 2 2 3 3
+--R (- 240a d + 576a b c d - 384a b c d + 128a b c )x
+--R *
+--R +-+ +-+
+--R \|a \|b
+--R /
+--R +--------+
+--R 5 4 2 4 2 3 3 +-+ +-+ | 2
+--R (40a b x + 160a b x + 128a b )\|a \|b \|b x + a
+--R +
+--R 6 6 2 5 4 3 4 2 4 3 +-+
+--R (- 8a b x - 104a b x - 224a b x - 128a b )\|b
+--R ,
+--R
+--R 3 2 3 2 3 2 4 2 4
+--R (150a b d - 360a b c d + 240a b c d)x
+--R +
+--R 4 3 3 2 2 2 3 2 2 5 3
+--R (600a b d - 1440a b c d + 960a b c d)x + 480a d
+--R +
+--R 4 2 3 2 2
+--R - 1152a b c d + 768a b c d
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|a \|b x + a
+--R +
+--R 3 3 3 2 4 2 5 2 6
+--R (- 30a b d + 72a b c d - 48a b c d)x
+--R +
+--R 4 2 3 3 3 2 2 4 2 4
+--R (- 390a b d + 936a b c d - 624a b c d)x
+--R +
+--R 5 3 4 2 2 3 3 2 2 6 3
+--R (- 840a b d + 2016a b c d - 1344a b c d)x - 480a d
+--R +
+--R 5 2 4 2 2
+--R 1152a b c d - 768a b c d
+--R *
+--R +--------+
+--R +---+ | 2 +---+ +-+
+--R \|- b \|b x + a - \|- b \|a
+--R atan(------------------------------)
+--R b x
+--R +
+--R 4 3 9 2 3 3 4 2 7
+--R - 2a b d x + (- 19a b d - 12a b c d )x
+--R +
+--R 3 2 3 2 3 2 4 2 5 3 5
+--R (43a b d - 180a b c d + 24a b c d - 8b c )x
+--R +
+--R 4 3 3 2 2 2 3 2 4 3 3
+--R (260a b d - 624a b c d + 288a b c d - 96a b c )x
+--R +
+--R 5 3 4 2 3 2 2 2 3 3
+--R (240a d - 576a b c d + 384a b c d - 128a b c )x
+--R *
+--R +--------+
+--R +---+ | 2
+--R \|- b \|b x + a
+--R +
+--R 4 3 9 2 3 3 4 2 7
+--R 10a b d x + (15a b d + 60a b c d )x
+--R +
+--R 3 2 3 2 3 2 4 2 5 3 5
+--R (- 143a b d + 420a b c d - 120a b c d + 40b c )x
+--R +
+--R 4 3 3 2 2 2 3 2 4 3 3
+--R (- 380a b d + 912a b c d - 480a b c d + 160a b c )x
+--R +
+--R 5 3 4 2 3 2 2 2 3 3
+--R (- 240a d + 576a b c d - 384a b c d + 128a b c )x
+--R *
+--R +---+ +-+
+--R \|- b \|a
+--R /
+--R +--------+
+--R 5 4 2 4 2 3 3 +---+ +-+ | 2
+--R (40a b x + 160a b x + 128a b )\|- b \|a \|b x + a
+--R +
+--R 6 6 2 5 4 3 4 2 4 3 +---+
+--R (- 8a b x - 104a b x - 224a b x - 128a b )\|- b
+--R ]
+--R Type: Union(List(Expression(Integer)),...)
+--E 471
+
+--S 472 of 994
+m0a:=a0.1-r0
+--R
+--R
+--R (4)
+--R 2 3 2 2 2
+--R (15a d - 36a b c d + 24b c d)
+--R *
+--R +--------+
+--R +-+ +-+ | 2 2 +-+ +-+
+--R (\|a \|b - b x)\|b x + a + (- b x - a)\|b + b x\|a
+--R log(--------------------------------------------------------)
+--R +--------+
+--R +-+ | 2
+--R \|a \|b x + a - a
+--R +
+--R +-+
+--R 2 3 2 2 2 x\|b
+--R (- 15a d + 36a b c d - 24b c d)atanh(-----------)
+--R +--------+
+--R | 2
+--R \|b x + a
+--R /
+--R 3 +-+
+--R 8b \|b
+--R Type: Expression(Integer)
+--E 472
+
+--S 473 of 994
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 473
+
+--S 474 of 994
+m0b:=a0.2-r0
+--R
+--R
+--R (6)
+--R +-+
+--R 2 3 2 2 2 +---+ x\|b
+--R (- 15a d + 36a b c d - 24b c d)\|- b atanh(-----------)
+--R +--------+
+--R | 2
+--R \|b x + a
+--R +
+--R +--------+
+--R +---+ | 2 +---+ +-+
+--R 2 3 2 2 2 +-+ \|- b \|b x + a - \|- b \|a
+--R (30a d - 72a b c d + 48b c d)\|b atan(------------------------------)
+--R b x
+--R /
+--R 3 +---+ +-+
+--R 8b \|- b \|b
+--R Type: Expression(Integer)
+--E 474
+
+--S 475 of 994
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 475
+
+)clear all
+
+--S 476 of 994
+t0:=(c+d*x^2)^2/(a+b*x^2)^(3/2)
+--R
+--R
+--R 2 4 2 2
+--R d x + 2c d x + c
+--R (1) ---------------------
+--R +--------+
+--R 2 | 2
+--R (b x + a)\|b x + a
+--R Type: Expression(Integer)
+--E 476
+
+--S 477 of 994
+r0a:=1/2*d*(4*b*c-3*a*d)*atanh(x*sqrt(b)/sqrt(a+b*x^2))/b^(5/2)+(b*c-a*d)^2*x/(a*b^2*sqrt(a+b*x^2))+1/2*d^2*x*sqrt(a+b*x^2)/b^2
+--R
+--R
+--R (2)
+--R +--------+ +-+
+--R 2 2 | 2 x\|b
+--R (- 3a d + 4a b c d)\|b x + a atanh(-----------)
+--R +--------+
+--R | 2
+--R \|b x + a
+--R +
+--R 2 3 2 2 2 2 +-+
+--R (a b d x + (3a d - 4a b c d + 2b c )x)\|b
+--R /
+--R +--------+
+--R 2 +-+ | 2
+--R 2a b \|b \|b x + a
+--R Type: Expression(Integer)
+--E 477
+
+--S 478 of 994
+r0b:=1/2*d*(4*b*c-3*a*d)*atanh(x*sqrt(b)/sqrt(a+b*x^2))/b^(5/2)+(b*c-a*d)*x*(c+d*x^2)/(a*b*sqrt(a+b*x^2))-1/2*d*(2*b*c-3*a*d)*x*sqrt(a+b*x^2)/(a*b^2)
+--R
+--R
+--R (3)
+--R +--------+ +-+
+--R 2 2 | 2 x\|b
+--R (- 3a d + 4a b c d)\|b x + a atanh(-----------)
+--R +--------+
+--R | 2
+--R \|b x + a
+--R +
+--R 2 3 2 2 2 2 +-+
+--R (a b d x + (3a d - 4a b c d + 2b c )x)\|b
+--R /
+--R +--------+
+--R 2 +-+ | 2
+--R 2a b \|b \|b x + a
+--R Type: Expression(Integer)
+--E 478
+
+--S 479 of 994
+a0:=integrate(t0,x)
+--R
+--R
+--R (4)
+--R [
+--R +--------+
+--R 2 2 2 2 3 2 2 +-+ | 2
+--R ((9a b d - 12a b c d)x + 12a d - 16a b c d)\|a \|b x + a
+--R +
+--R 2 2 2 3 4 3 2 2 2 2 4 2
+--R (- 3a b d + 4a b c d)x + (- 15a b d + 20a b c d)x - 12a d
+--R +
+--R 3
+--R 16a b c d
+--R *
+--R +--------+
+--R +-+ +-+ | 2 2 +-+ +-+
+--R (\|a \|b + b x)\|b x + a + (- b x - a)\|b - b x\|a
+--R log(--------------------------------------------------------)
+--R +--------+
+--R +-+ | 2
+--R \|a \|b x + a - a
+--R +
+--R 2 2 5 2 2 2 3 2 3
+--R - a b d x + (- 7a b d + 4a b c d - 2b c )x
+--R +
+--R 3 2 2 2 2
+--R (- 12a d + 16a b c d - 8a b c )x
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|b \|b x + a
+--R +
+--R 2 2 5 2 2 2 3 2 3
+--R 3a b d x + (13a b d - 12a b c d + 6b c )x
+--R +
+--R 3 2 2 2 2
+--R (12a d - 16a b c d + 8a b c )x
+--R *
+--R +-+ +-+
+--R \|a \|b
+--R /
+--R +--------+
+--R 3 2 2 2 +-+ +-+ | 2 4 4 2 3 2 3 2 +-+
+--R (6a b x + 8a b )\|a \|b \|b x + a + (- 2a b x - 10a b x - 8a b )\|b
+--R ,
+--R
+--R +--------+
+--R 2 2 2 2 3 2 2 +-+ | 2
+--R ((- 18a b d + 24a b c d)x - 24a d + 32a b c d)\|a \|b x + a
+--R +
+--R 2 2 2 3 4 3 2 2 2 2 4 2
+--R (6a b d - 8a b c d)x + (30a b d - 40a b c d)x + 24a d
+--R +
+--R 3
+--R - 32a b c d
+--R *
+--R +--------+
+--R +---+ | 2 +---+ +-+
+--R \|- b \|b x + a - \|- b \|a
+--R atan(------------------------------)
+--R b x
+--R +
+--R 2 2 5 2 2 2 3 2 3
+--R - a b d x + (- 7a b d + 4a b c d - 2b c )x
+--R +
+--R 3 2 2 2 2
+--R (- 12a d + 16a b c d - 8a b c )x
+--R *
+--R +--------+
+--R +---+ | 2
+--R \|- b \|b x + a
+--R +
+--R 2 2 5 2 2 2 3 2 3
+--R 3a b d x + (13a b d - 12a b c d + 6b c )x
+--R +
+--R 3 2 2 2 2
+--R (12a d - 16a b c d + 8a b c )x
+--R *
+--R +---+ +-+
+--R \|- b \|a
+--R /
+--R +--------+
+--R 3 2 2 2 +---+ +-+ | 2
+--R (6a b x + 8a b )\|- b \|a \|b x + a
+--R +
+--R 4 4 2 3 2 3 2 +---+
+--R (- 2a b x - 10a b x - 8a b )\|- b
+--R ]
+--R Type: Union(List(Expression(Integer)),...)
+--E 479
+
+--S 480 of 994
+m0a:=a0.1-r0a
+--R
+--R
+--R (5)
+--R 2
+--R (3a d - 4b c d)
+--R *
+--R +--------+
+--R +-+ +-+ | 2 2 +-+ +-+
+--R (\|a \|b + b x)\|b x + a + (- b x - a)\|b - b x\|a
+--R log(--------------------------------------------------------)
+--R +--------+
+--R +-+ | 2
+--R \|a \|b x + a - a
+--R +
+--R +-+
+--R 2 x\|b
+--R (3a d - 4b c d)atanh(-----------)
+--R +--------+
+--R | 2
+--R \|b x + a
+--R /
+--R 2 +-+
+--R 2b \|b
+--R Type: Expression(Integer)
+--E 480
+
+--S 481 of 994
+d0a:=D(m0a,x)
+--R
+--R
+--R (6) 0
+--R Type: Expression(Integer)
+--E 481
+
+--S 482 of 994
+m0b:=a0.2-r0a
+--R
+--R
+--R (7)
+--R +-+
+--R 2 +---+ x\|b
+--R (3a d - 4b c d)\|- b atanh(-----------)
+--R +--------+
+--R | 2
+--R \|b x + a
+--R +
+--R +--------+
+--R +---+ | 2 +---+ +-+
+--R 2 +-+ \|- b \|b x + a - \|- b \|a
+--R (- 6a d + 8b c d)\|b atan(------------------------------)
+--R b x
+--R /
+--R 2 +---+ +-+
+--R 2b \|- b \|b
+--R Type: Expression(Integer)
+--E 482
+
+--S 483 of 994
+d0b:=D(m0b,x)
+--R
+--R
+--R (8) 0
+--R Type: Expression(Integer)
+--E 483
+
+--S 484 of 994
+m0c:=a0.1-r0b
+--R
+--R
+--R (9)
+--R 2
+--R (3a d - 4b c d)
+--R *
+--R +--------+
+--R +-+ +-+ | 2 2 +-+ +-+
+--R (\|a \|b + b x)\|b x + a + (- b x - a)\|b - b x\|a
+--R log(--------------------------------------------------------)
+--R +--------+
+--R +-+ | 2
+--R \|a \|b x + a - a
+--R +
+--R +-+
+--R 2 x\|b
+--R (3a d - 4b c d)atanh(-----------)
+--R +--------+
+--R | 2
+--R \|b x + a
+--R /
+--R 2 +-+
+--R 2b \|b
+--R Type: Expression(Integer)
+--E 484
+
+--S 485 of 994
+d0c:=D(m0c,x)
+--R
+--R
+--R (10) 0
+--R Type: Expression(Integer)
+--E 485
+
+--S 486 of 994
+m0d:=a0.2-r0b
+--R
+--R
+--R (11)
+--R +-+
+--R 2 +---+ x\|b
+--R (3a d - 4b c d)\|- b atanh(-----------)
+--R +--------+
+--R | 2
+--R \|b x + a
+--R +
+--R +--------+
+--R +---+ | 2 +---+ +-+
+--R 2 +-+ \|- b \|b x + a - \|- b \|a
+--R (- 6a d + 8b c d)\|b atan(------------------------------)
+--R b x
+--R /
+--R 2 +---+ +-+
+--R 2b \|- b \|b
+--R Type: Expression(Integer)
+--E 486
+
+--S 487 of 994
+d0d:=D(m0d,x)
+--R
+--R
+--R (12) 0
+--R Type: Expression(Integer)
+--E 487
+
+)clear all
+
+--S 488 of 994
+t0:=(c+d*x^2)/(a+b*x^2)^(3/2)
+--R
+--R
+--R 2
+--R d x + c
+--R (1) ---------------------
+--R +--------+
+--R 2 | 2
+--R (b x + a)\|b x + a
+--R Type: Expression(Integer)
+--E 488
+
+--S 489 of 994
+r0:=d*atanh(x*sqrt(b)/sqrt(a+b*x^2))/b^(3/2)+(b*c-a*d)*x/(a*b*sqrt(a+b*x^2))
+--R
+--R
+--R +--------+ +-+
+--R | 2 x\|b +-+
+--R a d\|b x + a atanh(-----------) + (- a d + b c)x\|b
+--R +--------+
+--R | 2
+--R \|b x + a
+--R (2) -----------------------------------------------------
+--R +--------+
+--R +-+ | 2
+--R a b\|b \|b x + a
+--R Type: Expression(Integer)
+--E 489
+
+--S 490 of 994
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R +--------+
+--R +-+ | 2 2 2
+--R (a d\|a \|b x + a - a b d x - a d)
+--R *
+--R +--------+
+--R +-+ +-+ | 2 2 +-+ +-+
+--R (\|a \|b - b x)\|b x + a + (- b x - a)\|b + b x\|a
+--R log(--------------------------------------------------------)
+--R +--------+
+--R +-+ | 2
+--R \|a \|b x + a - a
+--R +
+--R +--------+
+--R +-+ | 2 +-+ +-+
+--R (a d - b c)x\|b \|b x + a + (- a d + b c)x\|a \|b
+--R /
+--R +--------+
+--R +-+ +-+ | 2 2 2 2 +-+
+--R a b\|a \|b \|b x + a + (- a b x - a b)\|b
+--R ,
+--R
+--R +--------+
+--R +-+ | 2 2 2
+--R (2a d\|a \|b x + a - 2a b d x - 2a d)
+--R *
+--R +--------+
+--R +---+ | 2 +---+ +-+
+--R \|- b \|b x + a - \|- b \|a
+--R atan(------------------------------)
+--R b x
+--R +
+--R +--------+
+--R +---+ | 2 +---+ +-+
+--R (a d - b c)x\|- b \|b x + a + (- a d + b c)x\|- b \|a
+--R /
+--R +--------+
+--R +---+ +-+ | 2 2 2 2 +---+
+--R a b\|- b \|a \|b x + a + (- a b x - a b)\|- b
+--R ]
+--R Type: Union(List(Expression(Integer)),...)
+--E 490
+
+--S 491 of 994
+m0a:=a0.1-r0
+--R
+--R
+--R (4)
+--R +--------+
+--R +-+ +-+ | 2 2 +-+ +-+
+--R (\|a \|b - b x)\|b x + a + (- b x - a)\|b + b x\|a
+--R d log(--------------------------------------------------------)
+--R +--------+
+--R +-+ | 2
+--R \|a \|b x + a - a
+--R +
+--R +-+
+--R x\|b
+--R - d atanh(-----------)
+--R +--------+
+--R | 2
+--R \|b x + a
+--R /
+--R +-+
+--R b\|b
+--R Type: Expression(Integer)
+--E 491
+
+--S 492 of 994
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 492
+
+--S 493 of 994
+m0b:=a0.2-r0
+--R
+--R
+--R (6)
+--R +--------+
+--R +-+ +---+ | 2 +---+ +-+
+--R +---+ x\|b +-+ \|- b \|b x + a - \|- b \|a
+--R - d\|- b atanh(-----------) + 2d\|b atan(------------------------------)
+--R +--------+ b x
+--R | 2
+--R \|b x + a
+--R ------------------------------------------------------------------------
+--R +---+ +-+
+--R b\|- b \|b
+--R Type: Expression(Integer)
+--E 493
+
+--S 494 of 994
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 494
+
+)clear all
+
+--S 495 of 994
+t0:=1/(a+b*x^2)^(3/2)
+--R
+--R
+--R 1
+--R (1) ---------------------
+--R +--------+
+--R 2 | 2
+--R (b x + a)\|b x + a
+--R Type: Expression(Integer)
+--E 495
+
+--S 496 of 994
+r0:=x/(a*sqrt(a+b*x^2))
+--R
+--R
+--R x
+--R (2) ------------
+--R +--------+
+--R | 2
+--R a\|b x + a
+--R Type: Expression(Integer)
+--E 496
+
+--S 497 of 994
+a0:=integrate(t0,x)
+--R
+--R
+--R +--------+
+--R | 2 +-+
+--R - x\|b x + a + x\|a
+--R (3) ------------------------------
+--R +--------+
+--R +-+ | 2 2 2
+--R a\|a \|b x + a - a b x - a
+--R Type: Union(Expression(Integer),...)
+--E 497
+
+--S 498 of 994
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 498
+
+--S 499 of 994
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 499
+
+)clear all
+
+--S 500 of 994
+t0:=1/((a+b*x^2)^(3/2)*(c+d*x^2))
+--R
+--R
+--R 1
+--R (1) -----------------------------------------
+--R +--------+
+--R 4 2 | 2
+--R (b d x + (a d + b c)x + a c)\|b x + a
+--R Type: Expression(Integer)
+--E 500
+
+--S 501 of 994
+r0:=-d*atanh(x*sqrt(b*c-a*d)/(sqrt(c)*sqrt(a+b*x^2)))/((b*c-a*d)^(3/2)*_
+ sqrt(c))+b*x/(a*(b*c-a*d)*sqrt(a+b*x^2))
+--R
+--R
+--R +--------+ +-----------+
+--R | 2 x\|- a d + b c +-----------+ +-+
+--R a d\|b x + a atanh(---------------) - b x\|- a d + b c \|c
+--R +--------+
+--R +-+ | 2
+--R \|c \|b x + a
+--R (2) ------------------------------------------------------------
+--R +--------+
+--R 2 +-----------+ +-+ | 2
+--R (a d - a b c)\|- a d + b c \|c \|b x + a
+--R Type: Expression(Integer)
+--E 501
+
+--S 502 of 994
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R +--------+
+--R +-+ | 2 2 2
+--R (a d\|a \|b x + a - a b d x - a d)
+--R *
+--R log
+--R +--------------+
+--R 2 | 2 +-+
+--R ((- 2a d + 4b c)x + 2a c)\|- a c d + b c \|a
+--R +
+--R 2 2 3 2 2
+--R (2a b c d - 2b c )x + (4a c d - 4a b c )x
+--R *
+--R +--------+
+--R | 2
+--R \|b x + a
+--R +
+--R 2 2 3 2 2 +-+
+--R ((- 4a b c d + 4b c )x + (- 4a c d + 4a b c )x)\|a
+--R +
+--R +--------------+
+--R 2 4 2 2 2 | 2
+--R ((a b d - 2b c)x + (2a d - 5a b c)x - 2a c)\|- a c d + b c
+--R /
+--R +--------+
+--R 2 +-+ | 2 4 2
+--R (2d x + 2c)\|a \|b x + a - b d x + (- 2a d - b c)x - 2a c
+--R +
+--R +--------------+ +--------+ +--------------+
+--R | 2 | 2 | 2 +-+
+--R 2b x\|- a c d + b c \|b x + a - 2b x\|- a c d + b c \|a
+--R /
+--R +--------------+ +--------+
+--R 2 | 2 +-+ | 2
+--R (2a d - 2a b c)\|- a c d + b c \|a \|b x + a
+--R +
+--R +--------------+
+--R 2 2 2 3 2 | 2
+--R ((- 2a b d + 2a b c)x - 2a d + 2a b c)\|- a c d + b c
+--R ,
+--R
+--R +--------+
+--R +-+ | 2 2 2
+--R (a d\|a \|b x + a - a b d x - a d)
+--R *
+--R +--------+
+--R 2 | 2 2 +-+
+--R ((a d - b c)x + a c)\|b x + a + (- a d x - a c)\|a
+--R atan(-------------------------------------------------------)
+--R +------------+
+--R 3 | 2
+--R b x \|a c d - b c
+--R +
+--R +------------+
+--R +--------+ +-+ | 2
+--R +-+ | 2 2 2 \|a \|a c d - b c
+--R (a d\|a \|b x + a - a b d x - a d)atan(-------------------)
+--R (a d - b c)x
+--R +
+--R +------------+ +--------+ +------------+
+--R | 2 | 2 +-+ | 2
+--R b x\|a c d - b c \|b x + a - b x\|a \|a c d - b c
+--R /
+--R +------------+ +--------+
+--R 2 +-+ | 2 | 2
+--R (a d - a b c)\|a \|a c d - b c \|b x + a
+--R +
+--R +------------+
+--R 2 2 2 3 2 | 2
+--R ((- a b d + a b c)x - a d + a b c)\|a c d - b c
+--R ]
+--R Type: Union(List(Expression(Integer)),...)
+--E 502
+
+--S 503 of 994
+m0a:=a0.1-r0
+--R
+--R
+--R (4)
+--R +-----------+ +-+
+--R d\|- a d + b c \|c
+--R *
+--R log
+--R +--------------+
+--R 2 | 2 +-+
+--R ((- 2a d + 4b c)x + 2a c)\|- a c d + b c \|a
+--R +
+--R 2 2 3 2 2
+--R (2a b c d - 2b c )x + (4a c d - 4a b c )x
+--R *
+--R +--------+
+--R | 2
+--R \|b x + a
+--R +
+--R 2 2 3 2 2 +-+
+--R ((- 4a b c d + 4b c )x + (- 4a c d + 4a b c )x)\|a
+--R +
+--R +--------------+
+--R 2 4 2 2 2 | 2
+--R ((a b d - 2b c)x + (2a d - 5a b c)x - 2a c)\|- a c d + b c
+--R /
+--R +--------+
+--R 2 +-+ | 2 4 2
+--R (2d x + 2c)\|a \|b x + a - b d x + (- 2a d - b c)x - 2a c
+--R +
+--R +--------------+ +-----------+
+--R | 2 x\|- a d + b c
+--R - 2d\|- a c d + b c atanh(---------------)
+--R +--------+
+--R +-+ | 2
+--R \|c \|b x + a
+--R /
+--R +--------------+
+--R | 2 +-----------+ +-+
+--R (2a d - 2b c)\|- a c d + b c \|- a d + b c \|c
+--R Type: Expression(Integer)
+--E 503
+
+--S 504 of 994
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 504
+
+--S 505 of 994
+m0b:=a0.2-r0
+--R
+--R
+--R (6)
+--R +------------+ +-----------+
+--R | 2 x\|- a d + b c
+--R - d\|a c d - b c atanh(---------------)
+--R +--------+
+--R +-+ | 2
+--R \|c \|b x + a
+--R +
+--R +-----------+ +-+
+--R d\|- a d + b c \|c
+--R *
+--R +--------+
+--R 2 | 2 2 +-+
+--R ((a d - b c)x + a c)\|b x + a + (- a d x - a c)\|a
+--R atan(-------------------------------------------------------)
+--R +------------+
+--R 3 | 2
+--R b x \|a c d - b c
+--R +
+--R +------------+
+--R +-+ | 2
+--R +-----------+ +-+ \|a \|a c d - b c
+--R d\|- a d + b c \|c atan(-------------------)
+--R (a d - b c)x
+--R /
+--R +------------+
+--R +-----------+ +-+ | 2
+--R (a d - b c)\|- a d + b c \|c \|a c d - b c
+--R Type: Expression(Integer)
+--E 505
+
+--S 506 of 994
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 506
+
+)clear all
+
+--S 507 of 994
+t0:=1/((a+b*x^2)^(3/2)*(c+d*x^2)^2)
+--R
+--R
+--R 1
+--R (1) ------------------------------------------------------------------
+--R +--------+
+--R 2 6 2 4 2 2 2 | 2
+--R (b d x + (a d + 2b c d)x + (2a c d + b c )x + a c )\|b x + a
+--R Type: Expression(Integer)
+--E 507
+
+--S 508 of 994
+r0:=-1/2*d*(4*b*c-a*d)*atanh(x*sqrt(b*c-a*d)/(sqrt(c)*sqrt(a+b*x^2)))/_
+ (c^(3/2)*(b*c-a*d)^(5/2))+b*x/(a*(b*c-a*d)*(c+d*x^2)*_
+ sqrt(a+b*x^2))+1/2*d*(2*b*c+a*d)*x*sqrt(a+b*x^2)/(a*c*(b*c-_
+ a*d)^2*(c+d*x^2))
+--R
+--R
+--R (2)
+--R +--------+
+--R 2 3 2 2 2 2 2 | 2
+--R ((a d - 4a b c d )x + a c d - 4a b c d)\|b x + a
+--R *
+--R +-----------+
+--R x\|- a d + b c
+--R atanh(---------------)
+--R +--------+
+--R +-+ | 2
+--R \|c \|b x + a
+--R +
+--R 2 2 3 2 2 2 2 +-----------+ +-+
+--R ((a b d + 2b c d)x + (a d + 2b c )x)\|- a d + b c \|c
+--R /
+--R 3 3 2 2 2 2 3 2 3 2 2 2 3 2 4
+--R ((2a c d - 4a b c d + 2a b c d)x + 2a c d - 4a b c d + 2a b c )
+--R *
+--R +--------+
+--R +-----------+ +-+ | 2
+--R \|- a d + b c \|c \|b x + a
+--R Type: Expression(Integer)
+--E 508
+
+--S 509 of 994
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R 2 3 2 2 4 3 3 2 2 2 2 2
+--R (3a b d - 12a b c d )x + (4a d - 13a b c d - 12a b c d)x
+--R +
+--R 3 2 2 2
+--R 4a c d - 16a b c d
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|a \|b x + a
+--R +
+--R 2 2 3 3 2 6 3 3 2 2 2 3 2 4
+--R (- a b d + 4a b c d )x + (- 5a b d + 19a b c d + 4a b c d)x
+--R +
+--R 4 3 3 2 2 2 2 2 4 2 3 2
+--R (- 4a d + 11a b c d + 20a b c d)x - 4a c d + 16a b c d
+--R *
+--R log
+--R +--------------+
+--R 2 | 2 +-+
+--R ((- 2a d + 4b c)x + 2a c)\|- a c d + b c \|a
+--R +
+--R 2 2 3 2 2
+--R (2a b c d - 2b c )x + (4a c d - 4a b c )x
+--R *
+--R +--------+
+--R | 2
+--R \|b x + a
+--R +
+--R 2 2 3 2 2 +-+
+--R ((- 4a b c d + 4b c )x + (- 4a c d + 4a b c )x)\|a
+--R +
+--R +--------------+
+--R 2 4 2 2 2 | 2
+--R ((a b d - 2b c)x + (2a d - 5a b c)x - 2a c)\|- a c d + b c
+--R /
+--R +--------+
+--R 2 +-+ | 2 4 2
+--R (2d x + 2c)\|a \|b x + a - b d x + (- 2a d - b c)x - 2a c
+--R +
+--R 2 2 3 5 2 2 2 3 2 3
+--R (- 2a b d - 4b c d)x + (- 10a b d - 16a b c d - 4b c )x
+--R +
+--R 3 2 2 2
+--R (- 8a d - 16a b c )x
+--R *
+--R +--------------+ +--------+
+--R | 2 | 2
+--R \|- a c d + b c \|b x + a
+--R +
+--R 2 2 3 5 2 2 2 3 2 3
+--R (6a b d + 12b c d)x + (14a b d + 16a b c d + 12b c )x
+--R +
+--R 3 2 2 2
+--R (8a d + 16a b c )x
+--R *
+--R +--------------+
+--R | 2 +-+
+--R \|- a c d + b c \|a
+--R /
+--R 3 3 2 2 2 2 3 3 4
+--R (12a b c d - 24a b c d + 12a b c d)x
+--R +
+--R 4 3 3 2 2 2 2 3 3 4 2 4 2 2
+--R (16a c d - 20a b c d - 8a b c d + 12a b c )x + 16a c d
+--R +
+--R 3 3 2 2 4
+--R - 32a b c d + 16a b c
+--R *
+--R +--------------+ +--------+
+--R | 2 +-+ | 2
+--R \|- a c d + b c \|a \|b x + a
+--R +
+--R 3 2 3 2 3 2 2 4 3 6
+--R (- 4a b c d + 8a b c d - 4a b c d)x
+--R +
+--R 4 3 3 2 2 2 2 3 3 4 4 4
+--R (- 20a b c d + 36a b c d - 12a b c d - 4a b c )x
+--R +
+--R 5 3 4 2 2 3 2 3 2 3 4 2 5 2 2
+--R (- 16a c d + 12a b c d + 24a b c d - 20a b c )x - 16a c d
+--R +
+--R 4 3 3 2 4
+--R 32a b c d - 16a b c
+--R *
+--R +--------------+
+--R | 2
+--R \|- a c d + b c
+--R ,
+--R
+--R 2 3 2 2 4 3 3 2 2 2 2 2
+--R (3a b d - 12a b c d )x + (4a d - 13a b c d - 12a b c d)x
+--R +
+--R 3 2 2 2
+--R 4a c d - 16a b c d
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|a \|b x + a
+--R +
+--R 2 2 3 3 2 6 3 3 2 2 2 3 2 4
+--R (- a b d + 4a b c d )x + (- 5a b d + 19a b c d + 4a b c d)x
+--R +
+--R 4 3 3 2 2 2 2 2 4 2 3 2
+--R (- 4a d + 11a b c d + 20a b c d)x - 4a c d + 16a b c d
+--R *
+--R +--------+
+--R 2 | 2 2 +-+
+--R ((a d - b c)x + a c)\|b x + a + (- a d x - a c)\|a
+--R atan(-------------------------------------------------------)
+--R +------------+
+--R 3 | 2
+--R b x \|a c d - b c
+--R +
+--R 2 3 2 2 4 3 3 2 2 2 2 2
+--R (3a b d - 12a b c d )x + (4a d - 13a b c d - 12a b c d)x
+--R +
+--R 3 2 2 2
+--R 4a c d - 16a b c d
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|a \|b x + a
+--R +
+--R 2 2 3 3 2 6 3 3 2 2 2 3 2 4
+--R (- a b d + 4a b c d )x + (- 5a b d + 19a b c d + 4a b c d)x
+--R +
+--R 4 3 3 2 2 2 2 2 4 2 3 2
+--R (- 4a d + 11a b c d + 20a b c d)x - 4a c d + 16a b c d
+--R *
+--R +------------+
+--R +-+ | 2
+--R \|a \|a c d - b c
+--R atan(-------------------)
+--R (a d - b c)x
+--R +
+--R 2 2 3 5 2 2 2 3 2 3
+--R (- a b d - 2b c d)x + (- 5a b d - 8a b c d - 2b c )x
+--R +
+--R 3 2 2 2
+--R (- 4a d - 8a b c )x
+--R *
+--R +------------+ +--------+
+--R | 2 | 2
+--R \|a c d - b c \|b x + a
+--R +
+--R 2 2 3 5 2 2 2 3 2 3
+--R (3a b d + 6b c d)x + (7a b d + 8a b c d + 6b c )x
+--R +
+--R 3 2 2 2
+--R (4a d + 8a b c )x
+--R *
+--R +------------+
+--R +-+ | 2
+--R \|a \|a c d - b c
+--R /
+--R 3 3 2 2 2 2 3 3 4
+--R (6a b c d - 12a b c d + 6a b c d)x
+--R +
+--R 4 3 3 2 2 2 2 3 3 4 2 4 2 2 3 3
+--R (8a c d - 10a b c d - 4a b c d + 6a b c )x + 8a c d - 16a b c d
+--R +
+--R 2 2 4
+--R 8a b c
+--R *
+--R +------------+ +--------+
+--R +-+ | 2 | 2
+--R \|a \|a c d - b c \|b x + a
+--R +
+--R 3 2 3 2 3 2 2 4 3 6
+--R (- 2a b c d + 4a b c d - 2a b c d)x
+--R +
+--R 4 3 3 2 2 2 2 3 3 4 4 4
+--R (- 10a b c d + 18a b c d - 6a b c d - 2a b c )x
+--R +
+--R 5 3 4 2 2 3 2 3 2 3 4 2 5 2 2
+--R (- 8a c d + 6a b c d + 12a b c d - 10a b c )x - 8a c d
+--R +
+--R 4 3 3 2 4
+--R 16a b c d - 8a b c
+--R *
+--R +------------+
+--R | 2
+--R \|a c d - b c
+--R ]
+--R Type: Union(List(Expression(Integer)),...)
+--E 509
+
+--S 510 of 994
+m0a:=a0.1-r0
+--R
+--R
+--R (4)
+--R 2 +-----------+ +-+
+--R (a d - 4b c d)\|- a d + b c \|c
+--R *
+--R log
+--R +--------------+
+--R 2 | 2 +-+
+--R ((- 2a d + 4b c)x + 2a c)\|- a c d + b c \|a
+--R +
+--R 2 2 3 2 2
+--R (2a b c d - 2b c )x + (4a c d - 4a b c )x
+--R *
+--R +--------+
+--R | 2
+--R \|b x + a
+--R +
+--R 2 2 3 2 2 +-+
+--R ((- 4a b c d + 4b c )x + (- 4a c d + 4a b c )x)\|a
+--R +
+--R +--------------+
+--R 2 4 2 2 2 | 2
+--R ((a b d - 2b c)x + (2a d - 5a b c)x - 2a c)\|- a c d + b c
+--R /
+--R +--------+
+--R 2 +-+ | 2 4 2
+--R (2d x + 2c)\|a \|b x + a - b d x + (- 2a d - b c)x - 2a c
+--R +
+--R +--------------+ +-----------+
+--R 2 | 2 x\|- a d + b c
+--R (- 2a d + 8b c d)\|- a c d + b c atanh(---------------)
+--R +--------+
+--R +-+ | 2
+--R \|c \|b x + a
+--R /
+--R +--------------+
+--R 2 2 2 2 3 | 2 +-----------+ +-+
+--R (4a c d - 8a b c d + 4b c )\|- a c d + b c \|- a d + b c \|c
+--R Type: Expression(Integer)
+--E 510
+
+--S 511 of 994
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 511
+
+--S 512 of 994
+m0b:=a0.2-r0
+--R
+--R
+--R (6)
+--R +------------+ +-----------+
+--R 2 | 2 x\|- a d + b c
+--R (- a d + 4b c d)\|a c d - b c atanh(---------------)
+--R +--------+
+--R +-+ | 2
+--R \|c \|b x + a
+--R +
+--R 2 +-----------+ +-+
+--R (a d - 4b c d)\|- a d + b c \|c
+--R *
+--R +--------+
+--R 2 | 2 2 +-+
+--R ((a d - b c)x + a c)\|b x + a + (- a d x - a c)\|a
+--R atan(-------------------------------------------------------)
+--R +------------+
+--R 3 | 2
+--R b x \|a c d - b c
+--R +
+--R +------------+
+--R +-+ | 2
+--R 2 +-----------+ +-+ \|a \|a c d - b c
+--R (a d - 4b c d)\|- a d + b c \|c atan(-------------------)
+--R (a d - b c)x
+--R /
+--R +------------+
+--R 2 2 2 2 3 +-----------+ +-+ | 2
+--R (2a c d - 4a b c d + 2b c )\|- a d + b c \|c \|a c d - b c
+--R Type: Expression(Integer)
+--E 512
+
+--S 513 of 994
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 513
+
+)clear all
+
+--S 514 of 994
+t0:=1/((a+b*x^2)^(3/2)*(c+d*x^2)^3)
+--R
+--R
+--R (1)
+--R 1
+--R /
+--R 3 8 3 2 6 2 2 4 2 3 2
+--R b d x + (a d + 3b c d )x + (3a c d + 3b c d)x + (3a c d + b c )x
+--R +
+--R 3
+--R a c
+--R *
+--R +--------+
+--R | 2
+--R \|b x + a
+--R Type: Expression(Integer)
+--E 514
+
+--S 515 of 994
+r0:=-3/8*d*(8*b^2*c^2-4*a*b*c*d+a^2*d^2)*atanh(x*sqrt(b*c-a*d)/_
+ (sqrt(c)*sqrt(a+b*x^2)))/(c^(5/2)*(b*c-a*d)^(7/2))+b*x/_
+ (a*(b*c-a*d)*(c+d*x^2)^2*sqrt(a+b*x^2))+1/4*d*(4*b*c+a*d)*_
+ x*sqrt(a+b*x^2)/(a*c*(b*c-a*d)^2*(c+d*x^2)^2)+1/8*d*(4*b*c-_
+ a*d)*(2*b*c+3*a*d)*x*sqrt(a+b*x^2)/(a*c^2*(b*c-a*d)^3*(c+d*x^2))
+--R
+--R
+--R (2)
+--R 3 5 2 4 2 2 3 4
+--R (3a d - 12a b c d + 24a b c d )x
+--R +
+--R 3 4 2 2 3 2 3 2 2 3 2 3 2 3 2
+--R (6a c d - 24a b c d + 48a b c d )x + 3a c d - 12a b c d
+--R +
+--R 2 4
+--R 24a b c d
+--R *
+--R +--------+ +-----------+
+--R | 2 x\|- a d + b c
+--R \|b x + a atanh(---------------)
+--R +--------+
+--R +-+ | 2
+--R \|c \|b x + a
+--R +
+--R 2 4 2 3 3 2 2 5
+--R (3a b d - 10a b c d - 8b c d )x
+--R +
+--R 3 4 2 3 2 2 2 3 3 3
+--R (3a d - 5a b c d - 12a b c d - 16b c d)x
+--R +
+--R 3 3 2 2 2 3 4
+--R (5a c d - 12a b c d - 8b c )x
+--R *
+--R +-----------+ +-+
+--R \|- a d + b c \|c
+--R /
+--R 4 2 5 3 3 4 2 2 4 3 3 5 2 4
+--R (8a c d - 24a b c d + 24a b c d - 8a b c d )x
+--R +
+--R 4 3 4 3 4 3 2 2 5 2 3 6 2 4 4 3
+--R (16a c d - 48a b c d + 48a b c d - 16a b c d)x + 8a c d
+--R +
+--R 3 5 2 2 2 6 3 7
+--R - 24a b c d + 24a b c d - 8a b c
+--R *
+--R +--------+
+--R +-----------+ +-+ | 2
+--R \|- a d + b c \|c \|b x + a
+--R Type: Expression(Integer)
+--E 515
+
+--S 516 of 994
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R 3 2 5 2 3 4 4 2 3 8
+--R (15a b d - 60a b c d + 120a b c d )x
+--R +
+--R 4 5 3 2 4 2 3 2 3 4 3 2 6
+--R (60a b d - 210a b c d + 360a b c d + 240a b c d )x
+--R +
+--R 5 5 4 4 3 2 2 3 2 3 3 2 4 4 4
+--R (48a d - 72a b c d - 81a b c d + 900a b c d + 120a b c d)x
+--R +
+--R 5 4 4 2 3 3 2 3 2 2 3 4 2
+--R (96a c d - 324a b c d + 528a b c d + 480a b c d)x
+--R +
+--R 5 2 3 4 3 2 3 2 4
+--R 48a c d - 192a b c d + 384a b c d
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|a \|b x + a
+--R +
+--R 3 3 5 2 4 4 5 2 3 10
+--R (- 3a b d + 12a b c d - 24a b c d )x
+--R +
+--R 4 2 5 3 3 4 2 4 2 3 5 3 2 8
+--R (- 39a b d + 150a b c d - 288a b c d - 48a b c d )x
+--R +
+--R 5 5 4 2 4 3 3 2 3 2 4 3 2
+--R - 84a b d + 258a b c d - 363a b c d - 612a b c d
+--R +
+--R 5 4
+--R - 24a b c d
+--R *
+--R 6
+--R x
+--R +
+--R 6 5 5 4 4 2 2 3 3 3 3 2 2 4 4 4
+--R (- 48a d + 24a b c d + 249a b c d - 1188a b c d - 312a b c d)x
+--R +
+--R 6 4 5 2 3 4 2 3 2 3 3 4 2 6 2 3
+--R (- 96a c d + 300a b c d - 432a b c d - 672a b c d)x - 48a c d
+--R +
+--R 5 3 2 4 2 4
+--R 192a b c d - 384a b c d
+--R *
+--R log
+--R +--------------+
+--R 2 | 2 +-+
+--R ((- 2a d + 4b c)x + 2a c)\|- a c d + b c \|a
+--R +
+--R 2 2 3 2 2
+--R (2a b c d - 2b c )x + (4a c d - 4a b c )x
+--R *
+--R +--------+
+--R | 2
+--R \|b x + a
+--R +
+--R 2 2 3 2 2 +-+
+--R ((- 4a b c d + 4b c )x + (- 4a c d + 4a b c )x)\|a
+--R +
+--R +--------------+
+--R 2 4 2 2 2 | 2
+--R ((a b d - 2b c)x + (2a d - 5a b c)x - 2a c)\|- a c d + b c
+--R /
+--R +--------+
+--R 2 +-+ | 2 4 2
+--R (2d x + 2c)\|a \|b x + a - b d x + (- 2a d - b c)x - 2a c
+--R +
+--R 2 3 4 4 3 5 2 2 9
+--R (- 6a b d + 20a b c d + 16b c d )x
+--R +
+--R 3 2 4 2 3 3 4 2 2 5 3 7
+--R (- 78a b d + 250a b c d + 216a b c d + 32b c d)x
+--R +
+--R 4 4 3 2 3 2 3 2 2 4 3 5 4 5
+--R (- 168a b d + 430a b c d + 568a b c d + 384a b c d + 16b c )x
+--R +
+--R 5 4 4 3 3 2 2 2 2 3 3 4 4 3
+--R (- 96a d + 40a b c d + 672a b c d + 512a b c d + 192a b c )x
+--R +
+--R 5 3 4 2 2 2 3 4
+--R (- 160a c d + 384a b c d + 256a b c )x
+--R *
+--R +--------------+ +--------+
+--R | 2 | 2
+--R \|- a c d + b c \|b x + a
+--R +
+--R 2 3 4 4 3 5 2 2 9
+--R (30a b d - 100a b c d - 80b c d )x
+--R +
+--R 3 2 4 2 3 3 4 2 2 5 3 7
+--R (150a b d - 450a b c d - 440a b c d - 160b c d)x
+--R +
+--R 4 4 3 2 3 2 3 2 2 4 3 5 4 5
+--R (216a b d - 470a b c d - 856a b c d - 640a b c d - 80b c )x
+--R +
+--R 5 4 4 3 3 2 2 2 2 3 3 4 4 3
+--R (96a d + 40a b c d - 864a b c d - 512a b c d - 320a b c )x
+--R +
+--R 5 3 4 2 2 2 3 4
+--R (160a c d - 384a b c d - 256a b c )x
+--R *
+--R +--------------+
+--R | 2 +-+
+--R \|- a c d + b c \|a
+--R /
+--R 4 2 2 5 3 3 3 4 2 4 4 3 5 5 2 8
+--R (80a b c d - 240a b c d + 240a b c d - 80a b c d )x
+--R +
+--R 5 2 5 4 2 3 4 3 3 4 3 2 4 5 2
+--R 320a b c d - 800a b c d + 480a b c d + 160a b c d
+--R +
+--R 5 6
+--R - 160a b c d
+--R *
+--R 6
+--R x
+--R +
+--R 6 2 5 5 3 4 4 2 4 3 3 3 5 2
+--R 256a c d - 128a b c d - 1072a b c d + 1424a b c d
+--R +
+--R 2 4 6 5 7
+--R - 400a b c d - 80a b c
+--R *
+--R 4
+--R x
+--R +
+--R 6 3 4 5 4 3 4 2 5 2 3 3 6 2 4 7 2
+--R (512a c d - 1216a b c d + 576a b c d + 448a b c d - 320a b c )x
+--R +
+--R 6 4 3 5 5 2 4 2 6 3 3 7
+--R 256a c d - 768a b c d + 768a b c d - 256a b c
+--R *
+--R +--------------+ +--------+
+--R | 2 +-+ | 2
+--R \|- a c d + b c \|a \|b x + a
+--R +
+--R 4 3 2 5 3 4 3 4 2 5 4 3 6 5 2 10
+--R (- 16a b c d + 48a b c d - 48a b c d + 16a b c d )x
+--R +
+--R 5 2 2 5 4 3 3 4 3 4 4 3 2 5 5 2
+--R - 208a b c d + 592a b c d - 528a b c d + 112a b c d
+--R +
+--R 6 6
+--R 32a b c d
+--R *
+--R 8
+--R x
+--R +
+--R 6 2 5 5 2 3 4 4 3 4 3 3 4 5 2
+--R - 448a b c d + 928a b c d - 112a b c d - 752a b c d
+--R +
+--R 2 5 6 6 7
+--R 368a b c d + 16a b c
+--R *
+--R 6
+--R x
+--R +
+--R 7 2 5 6 3 4 5 2 4 3 4 3 5 2
+--R - 256a c d - 128a b c d + 1712a b c d - 1808a b c d
+--R +
+--R 3 4 6 2 5 7
+--R 272a b c d + 208a b c
+--R *
+--R 4
+--R x
+--R +
+--R 7 3 4 6 4 3 5 2 5 2 4 3 6
+--R - 512a c d + 1088a b c d - 192a b c d - 832a b c d
+--R +
+--R 3 4 7
+--R 448a b c
+--R *
+--R 2
+--R x
+--R +
+--R 7 4 3 6 5 2 5 2 6 4 3 7
+--R - 256a c d + 768a b c d - 768a b c d + 256a b c
+--R *
+--R +--------------+
+--R | 2
+--R \|- a c d + b c
+--R ,
+--R
+--R 3 2 5 2 3 4 4 2 3 8
+--R (15a b d - 60a b c d + 120a b c d )x
+--R +
+--R 4 5 3 2 4 2 3 2 3 4 3 2 6
+--R (60a b d - 210a b c d + 360a b c d + 240a b c d )x
+--R +
+--R 5 5 4 4 3 2 2 3 2 3 3 2 4 4 4
+--R (48a d - 72a b c d - 81a b c d + 900a b c d + 120a b c d)x
+--R +
+--R 5 4 4 2 3 3 2 3 2 2 3 4 2
+--R (96a c d - 324a b c d + 528a b c d + 480a b c d)x
+--R +
+--R 5 2 3 4 3 2 3 2 4
+--R 48a c d - 192a b c d + 384a b c d
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|a \|b x + a
+--R +
+--R 3 3 5 2 4 4 5 2 3 10
+--R (- 3a b d + 12a b c d - 24a b c d )x
+--R +
+--R 4 2 5 3 3 4 2 4 2 3 5 3 2 8
+--R (- 39a b d + 150a b c d - 288a b c d - 48a b c d )x
+--R +
+--R 5 5 4 2 4 3 3 2 3 2 4 3 2
+--R - 84a b d + 258a b c d - 363a b c d - 612a b c d
+--R +
+--R 5 4
+--R - 24a b c d
+--R *
+--R 6
+--R x
+--R +
+--R 6 5 5 4 4 2 2 3 3 3 3 2 2 4 4 4
+--R (- 48a d + 24a b c d + 249a b c d - 1188a b c d - 312a b c d)x
+--R +
+--R 6 4 5 2 3 4 2 3 2 3 3 4 2 6 2 3
+--R (- 96a c d + 300a b c d - 432a b c d - 672a b c d)x - 48a c d
+--R +
+--R 5 3 2 4 2 4
+--R 192a b c d - 384a b c d
+--R *
+--R +--------+
+--R 2 | 2 2 +-+
+--R ((a d - b c)x + a c)\|b x + a + (- a d x - a c)\|a
+--R atan(-------------------------------------------------------)
+--R +------------+
+--R 3 | 2
+--R b x \|a c d - b c
+--R +
+--R 3 2 5 2 3 4 4 2 3 8
+--R (15a b d - 60a b c d + 120a b c d )x
+--R +
+--R 4 5 3 2 4 2 3 2 3 4 3 2 6
+--R (60a b d - 210a b c d + 360a b c d + 240a b c d )x
+--R +
+--R 5 5 4 4 3 2 2 3 2 3 3 2 4 4 4
+--R (48a d - 72a b c d - 81a b c d + 900a b c d + 120a b c d)x
+--R +
+--R 5 4 4 2 3 3 2 3 2 2 3 4 2
+--R (96a c d - 324a b c d + 528a b c d + 480a b c d)x
+--R +
+--R 5 2 3 4 3 2 3 2 4
+--R 48a c d - 192a b c d + 384a b c d
+--R *
+--R +--------+
+--R +-+ | 2
+--R \|a \|b x + a
+--R +
+--R 3 3 5 2 4 4 5 2 3 10
+--R (- 3a b d + 12a b c d - 24a b c d )x
+--R +
+--R 4 2 5 3 3 4 2 4 2 3 5 3 2 8
+--R (- 39a b d + 150a b c d - 288a b c d - 48a b c d )x
+--R +
+--R 5 5 4 2 4 3 3 2 3 2 4 3 2
+--R - 84a b d + 258a b c d - 363a b c d - 612a b c d
+--R +
+--R 5 4
+--R - 24a b c d
+--R *
+--R 6
+--R x
+--R +
+--R 6 5 5 4 4 2 2 3 3 3 3 2 2 4 4 4
+--R (- 48a d + 24a b c d + 249a b c d - 1188a b c d - 312a b c d)x
+--R +
+--R 6 4 5 2 3 4 2 3 2 3 3 4 2 6 2 3
+--R (- 96a c d + 300a b c d - 432a b c d - 672a b c d)x - 48a c d
+--R +
+--R 5 3 2 4 2 4
+--R 192a b c d - 384a b c d
+--R *
+--R +------------+
+--R +-+ | 2
+--R \|a \|a c d - b c
+--R atan(-------------------)
+--R (a d - b c)x
+--R +
+--R 2 3 4 4 3 5 2 2 9
+--R (- 3a b d + 10a b c d + 8b c d )x
+--R +
+--R 3 2 4 2 3 3 4 2 2 5 3 7
+--R (- 39a b d + 125a b c d + 108a b c d + 16b c d)x
+--R +
+--R 4 4 3 2 3 2 3 2 2 4 3 5 4 5
+--R (- 84a b d + 215a b c d + 284a b c d + 192a b c d + 8b c )x
+--R +
+--R 5 4 4 3 3 2 2 2 2 3 3 4 4 3
+--R (- 48a d + 20a b c d + 336a b c d + 256a b c d + 96a b c )x
+--R +
+--R 5 3 4 2 2 2 3 4
+--R (- 80a c d + 192a b c d + 128a b c )x
+--R *
+--R +------------+ +--------+
+--R | 2 | 2
+--R \|a c d - b c \|b x + a
+--R +
+--R 2 3 4 4 3 5 2 2 9
+--R (15a b d - 50a b c d - 40b c d )x
+--R +
+--R 3 2 4 2 3 3 4 2 2 5 3 7
+--R (75a b d - 225a b c d - 220a b c d - 80b c d)x
+--R +
+--R 4 4 3 2 3 2 3 2 2 4 3 5 4 5
+--R (108a b d - 235a b c d - 428a b c d - 320a b c d - 40b c )x
+--R +
+--R 5 4 4 3 3 2 2 2 2 3 3 4 4 3
+--R (48a d + 20a b c d - 432a b c d - 256a b c d - 160a b c )x
+--R +
+--R 5 3 4 2 2 2 3 4
+--R (80a c d - 192a b c d - 128a b c )x
+--R *
+--R +------------+
+--R +-+ | 2
+--R \|a \|a c d - b c
+--R /
+--R 4 2 2 5 3 3 3 4 2 4 4 3 5 5 2 8
+--R (40a b c d - 120a b c d + 120a b c d - 40a b c d )x
+--R +
+--R 5 2 5 4 2 3 4 3 3 4 3 2 4 5 2
+--R 160a b c d - 400a b c d + 240a b c d + 80a b c d
+--R +
+--R 5 6
+--R - 80a b c d
+--R *
+--R 6
+--R x
+--R +
+--R 6 2 5 5 3 4 4 2 4 3 3 3 5 2 2 4 6
+--R 128a c d - 64a b c d - 536a b c d + 712a b c d - 200a b c d
+--R +
+--R 5 7
+--R - 40a b c
+--R *
+--R 4
+--R x
+--R +
+--R 6 3 4 5 4 3 4 2 5 2 3 3 6 2 4 7 2
+--R (256a c d - 608a b c d + 288a b c d + 224a b c d - 160a b c )x
+--R +
+--R 6 4 3 5 5 2 4 2 6 3 3 7
+--R 128a c d - 384a b c d + 384a b c d - 128a b c
+--R *
+--R +------------+ +--------+
+--R +-+ | 2 | 2
+--R \|a \|a c d - b c \|b x + a
+--R +
+--R 4 3 2 5 3 4 3 4 2 5 4 3 6 5 2 10
+--R (- 8a b c d + 24a b c d - 24a b c d + 8a b c d )x
+--R +
+--R 5 2 2 5 4 3 3 4 3 4 4 3 2 5 5 2
+--R - 104a b c d + 296a b c d - 264a b c d + 56a b c d
+--R +
+--R 6 6
+--R 16a b c d
+--R *
+--R 8
+--R x
+--R +
+--R 6 2 5 5 2 3 4 4 3 4 3 3 4 5 2
+--R - 224a b c d + 464a b c d - 56a b c d - 376a b c d
+--R +
+--R 2 5 6 6 7
+--R 184a b c d + 8a b c
+--R *
+--R 6
+--R x
+--R +
+--R 7 2 5 6 3 4 5 2 4 3 4 3 5 2
+--R - 128a c d - 64a b c d + 856a b c d - 904a b c d
+--R +
+--R 3 4 6 2 5 7
+--R 136a b c d + 104a b c
+--R *
+--R 4
+--R x
+--R +
+--R 7 3 4 6 4 3 5 2 5 2 4 3 6 3 4 7 2
+--R (- 256a c d + 544a b c d - 96a b c d - 416a b c d + 224a b c )x
+--R +
+--R 7 4 3 6 5 2 5 2 6 4 3 7
+--R - 128a c d + 384a b c d - 384a b c d + 128a b c
+--R *
+--R +------------+
+--R | 2
+--R \|a c d - b c
+--R ]
+--R Type: Union(List(Expression(Integer)),...)
+--E 516
+
+--S 517 of 994
+m0a:=a0.1-r0
+--R
+--R
+--R (4)
+--R 2 3 2 2 2 +-----------+ +-+
+--R (3a d - 12a b c d + 24b c d)\|- a d + b c \|c
+--R *
+--R log
+--R +--------------+
+--R 2 | 2 +-+
+--R ((- 2a d + 4b c)x + 2a c)\|- a c d + b c \|a
+--R +
+--R 2 2 3 2 2
+--R (2a b c d - 2b c )x + (4a c d - 4a b c )x
+--R *
+--R +--------+
+--R | 2
+--R \|b x + a
+--R +
+--R 2 2 3 2 2 +-+
+--R ((- 4a b c d + 4b c )x + (- 4a c d + 4a b c )x)\|a
+--R +
+--R +--------------+
+--R 2 4 2 2 2 | 2
+--R ((a b d - 2b c)x + (2a d - 5a b c)x - 2a c)\|- a c d + b c
+--R /
+--R +--------+
+--R 2 +-+ | 2 4 2
+--R (2d x + 2c)\|a \|b x + a - b d x + (- 2a d - b c)x - 2a c
+--R +
+--R +--------------+ +-----------+
+--R 2 3 2 2 2 | 2 x\|- a d + b c
+--R (- 6a d + 24a b c d - 48b c d)\|- a c d + b c atanh(---------------)
+--R +--------+
+--R +-+ | 2
+--R \|c \|b x + a
+--R /
+--R +--------------+
+--R 3 2 3 2 3 2 2 4 3 5 | 2
+--R (16a c d - 48a b c d + 48a b c d - 16b c )\|- a c d + b c
+--R *
+--R +-----------+ +-+
+--R \|- a d + b c \|c
+--R Type: Expression(Integer)
+--E 517
+
+--S 518 of 994
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 518
+
+--S 519 of 994
+m0b:=a0.2-r0
+--R
+--R
+--R (6)
+--R +------------+ +-----------+
+--R 2 3 2 2 2 | 2 x\|- a d + b c
+--R (- 3a d + 12a b c d - 24b c d)\|a c d - b c atanh(---------------)
+--R +--------+
+--R +-+ | 2
+--R \|c \|b x + a
+--R +
+--R 2 3 2 2 2 +-----------+ +-+
+--R (3a d - 12a b c d + 24b c d)\|- a d + b c \|c
+--R *
+--R +--------+
+--R 2 | 2 2 +-+
+--R ((a d - b c)x + a c)\|b x + a + (- a d x - a c)\|a
+--R atan(-------------------------------------------------------)
+--R +------------+
+--R 3 | 2
+--R b x \|a c d - b c
+--R +
+--R +------------+
+--R +-+ | 2
+--R 2 3 2 2 2 +-----------+ +-+ \|a \|a c d - b c
+--R (3a d - 12a b c d + 24b c d)\|- a d + b c \|c atan(-------------------)
+--R (a d - b c)x
+--R /
+--R +------------+
+--R 3 2 3 2 3 2 2 4 3 5 +-----------+ +-+ | 2
+--R (8a c d - 24a b c d + 24a b c d - 8b c )\|- a d + b c \|c \|a c d - b c
+--R Type: Expression(Integer)
+--E 519
+
+--S 520 of 994
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 520
+
+)clear all
+
+--S 521 of 994
+t0:=1/((b*c/d+b*x^2)*sqrt(c+d*x^2))
+--R
+--R
+--R d
+--R (1) -------------------------
+--R +--------+
+--R 2 | 2
+--R (b d x + b c)\|d x + c
+--R Type: Expression(Integer)
+--E 521
+
+--S 522 of 994
+r0:=d*x/(b*c*sqrt(c+d*x^2))
+--R
+--R
+--R d x
+--R (2) --------------
+--R +--------+
+--R | 2
+--R b c\|d x + c
+--R Type: Expression(Integer)
+--E 522
+
+--S 523 of 994
+a0:=integrate(t0,x)
+--R
+--R
+--R +--------+
+--R | 2 +-+
+--R - d x\|d x + c + d x\|c
+--R (3) ------------------------------------
+--R +--------+
+--R +-+ | 2 2 2
+--R b c\|c \|d x + c - b c d x - b c
+--R Type: Union(Expression(Integer),...)
+--E 523
+
+--S 524 of 994
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 524
+
+--S 525 of 994
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 525
+
+)clear all
+
+--S 526 of 994
+t0:=1/((1+x^2)*sqrt(1-x^2))
+--R
+--R
+--R 1
+--R (1) -------------------
+--R +--------+
+--R 2 | 2
+--R (x + 1)\|- x + 1
+--R Type: Expression(Integer)
+--E 526
+
+--S 527 of 994
+r0:=atan(x*sqrt(2)/sqrt(1-x^2))/sqrt(2)
+--R
+--R
+--R +-+
+--R x\|2
+--R atan(-----------)
+--R +--------+
+--R | 2
+--R \|- x + 1
+--R (2) -----------------
+--R +-+
+--R \|2
+--R Type: Expression(Integer)
+--E 527
+
+--S 528 of 994
+a0:=integrate(t0,x)
+--R
+--R
+--R +--------+
+--R 2 | 2 2 +-+
+--R (2x + 1)\|- x + 1 - x - 1 \|2
+--R - atan(-----------------------------) + atan(----)
+--R 3 +-+ 2x
+--R x \|2
+--R (3) --------------------------------------------------
+--R +-+
+--R \|2
+--R Type: Union(Expression(Integer),...)
+--E 528
+
+--S 529 of 994
+m0:=a0-r0
+--R
+--R
+--R +--------+
+--R 2 | 2 2 +-+ +-+
+--R (2x + 1)\|- x + 1 - x - 1 x\|2 \|2
+--R - atan(-----------------------------) - atan(-----------) + atan(----)
+--R 3 +-+ +--------+ 2x
+--R x \|2 | 2
+--R \|- x + 1
+--R (4) ----------------------------------------------------------------------
+--R +-+
+--R \|2
+--R Type: Expression(Integer)
+--E 529
+
+--S 530 of 994
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 530
+
+)clear all
+
+--S 531 of 994
+t0:=1/((a+b*x^2)*sqrt(c+d*x^2))
+--R
+--R
+--R 1
+--R (1) ---------------------
+--R +--------+
+--R 2 | 2
+--R (b x + a)\|d x + c
+--R Type: Expression(Integer)
+--E 531
+
+--S 532 of 994
+r0:=atan(x*sqrt(b*c-a*d)/(sqrt(a)*sqrt(c+d*x^2)))/(sqrt(a)*sqrt(b*c-a*d))
+--R
+--R
+--R +-----------+
+--R x\|- a d + b c
+--R atan(---------------)
+--R +--------+
+--R +-+ | 2
+--R \|a \|d x + c
+--R (2) ---------------------
+--R +-----------+ +-+
+--R \|- a d + b c \|a
+--R Type: Expression(Integer)
+--E 532
+
+--S 533 of 994
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R log
+--R +-----------+
+--R 2 +-+ | 2
+--R ((4a d - 2b c)x + 2a c)\|c \|a d - a b c
+--R +
+--R 2 2 3 2 2
+--R (- 2a d + 2a b c d)x + (- 4a c d + 4a b c )x
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R +-----------+
+--R 2 4 2 2 2 | 2
+--R ((- 2a d + b c d)x + (- 5a c d + 2b c )x - 2a c )\|a d - a b c
+--R +
+--R 2 2 3 2 2 +-+
+--R ((4a d - 4a b c d)x + (4a c d - 4a b c )x)\|c
+--R /
+--R +--------+
+--R 2 +-+ | 2 4 2
+--R (2b x + 2a)\|c \|d x + c - b d x + (- a d - 2b c)x - 2a c
+--R /
+--R +-----------+
+--R | 2
+--R 2\|a d - a b c
+--R ,
+--R
+--R +--------+
+--R 2 | 2 2 +-+
+--R ((a d - b c)x - a c)\|d x + c + (b c x + a c)\|c
+--R - atan(-----------------------------------------------------)
+--R +-------------+
+--R 3 | 2
+--R d x \|- a d + a b c
+--R +
+--R +-------------+
+--R | 2 +-+
+--R \|- a d + a b c \|c
+--R - atan(--------------------)
+--R (a d - b c)x
+--R /
+--R +-------------+
+--R | 2
+--R \|- a d + a b c
+--R ]
+--R Type: Union(List(Expression(Integer)),...)
+--E 533
+
+--S 534 of 994
+m0a:=a0.1-r0
+--R
+--R
+--R (4)
+--R +-----------+ +-+
+--R \|- a d + b c \|a
+--R *
+--R log
+--R +-----------+
+--R 2 +-+ | 2
+--R ((4a d - 2b c)x + 2a c)\|c \|a d - a b c
+--R +
+--R 2 2 3 2 2
+--R (- 2a d + 2a b c d)x + (- 4a c d + 4a b c )x
+--R *
+--R +--------+
+--R | 2
+--R \|d x + c
+--R +
+--R 2 4 2 2 2
+--R ((- 2a d + b c d)x + (- 5a c d + 2b c )x - 2a c )
+--R *
+--R +-----------+
+--R | 2
+--R \|a d - a b c
+--R +
+--R 2 2 3 2 2 +-+
+--R ((4a d - 4a b c d)x + (4a c d - 4a b c )x)\|c
+--R /
+--R +--------+
+--R 2 +-+ | 2 4 2
+--R (2b x + 2a)\|c \|d x + c - b d x + (- a d - 2b c)x - 2a c
+--R +
+--R +-----------+ +-----------+
+--R | 2 x\|- a d + b c
+--R - 2\|a d - a b c atan(---------------)
+--R +--------+
+--R +-+ | 2
+--R \|a \|d x + c
+--R /
+--R +-----------+
+--R +-----------+ +-+ | 2
+--R 2\|- a d + b c \|a \|a d - a b c
+--R Type: Expression(Integer)
+--E 534
+
+--S 535 of 994
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 535
+
+--S 536 of 994
+m0b:=a0.2-r0
+--R
+--R
+--R (6)
+--R -
+--R +-----------+ +-+
+--R \|- a d + b c \|a
+--R *
+--R +--------+
+--R 2 | 2 2 +-+
+--R ((a d - b c)x - a c)\|d x + c + (b c x + a c)\|c
+--R atan(-----------------------------------------------------)
+--R +-------------+
+--R 3 | 2
+--R d x \|- a d + a b c
+--R +
+--R +-------------+
+--R | 2 +-+
+--R +-----------+ +-+ \|- a d + a b c \|c
+--R - \|- a d + b c \|a atan(--------------------)
+--R (a d - b c)x
+--R +
+--R +-------------+ +-----------+
+--R | 2 x\|- a d + b c
+--R - \|- a d + a b c atan(---------------)
+--R +--------+
+--R +-+ | 2
+--R \|a \|d x + c
+--R /
+--R +-------------+
+--R | 2 +-----------+ +-+
+--R \|- a d + a b c \|- a d + b c \|a
+--R Type: Expression(Integer)
+--E 536
+
+--S 537 of 994
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 537
+
+)clear all
+
+--S 538 of 994
+t0:=(-1+x^2)/(1+x^2)^(3/2)
+--R
+--R
+--R 2
+--R x - 1
+--R (1) -----------------
+--R +------+
+--R 2 | 2
+--R (x + 1)\|x + 1
+--R Type: Expression(Integer)
+--E 538
+
+--S 539 of 994
+r0:=asinh(x)-2*x/sqrt(1+x^2)
+--R
+--R
+--R +------+
+--R | 2
+--R asinh(x)\|x + 1 - 2x
+--R (2) ----------------------
+--R +------+
+--R | 2
+--R \|x + 1
+--R Type: Expression(Integer)
+--E 539
+
+--S 540 of 994
+a0:=integrate(t0,x)
+--R
+--R
+--R +------+ +------+
+--R | 2 2 | 2
+--R (- x\|x + 1 + x + 1)log(\|x + 1 - x) + 2
+--R (3) ---------------------------------------------
+--R +------+
+--R | 2 2
+--R x\|x + 1 - x - 1
+--R Type: Union(Expression(Integer),...)
+--E 540
+
+--S 541 of 994
+m0:=a0-r0
+--R
+--R
+--R +------+
+--R | 2
+--R (4) - log(\|x + 1 - x) - asinh(x) - 2
+--R Type: Expression(Integer)
+--E 541
+
+--S 542 of 994
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 542
+
+)clear all
+
+--S 543 of 994
+t0:=(a+b*x^2)^(5/2)*(c+d*x^2)^(1/2)
+--R
+--R
+--R +--------+ +--------+
+--R 2 4 2 2 | 2 | 2
+--R (1) (b x + 2a b x + a )\|b x + a \|d x + c
+--R Type: Expression(Integer)
+--E 543
+
+--S 544 of 994
+--r0:=1/7*b*x*(a+b*x^2)^(3/2)*(c+d*x^2)^(3/2)/d-2/35*(2*b*c-5*a*d)*_
+-- x*(a+b*x^2)^(3/2)*sqrt(c+d*x^2)/d-1/105*(4*b^2*c^2-13*a*b*c*d-_
+-- 15*a^2*d^2)*x*sqrt(a+b*x^2)*sqrt(c+d*x^2)/d^2+1/105*(8*b^3*c^3-_
+-- 33*a*b^2*c^2*d+58*a^2*b*c*d^2+15*a^3*d^3)*elliptic_e(asin(x*_
+-- sqrt(-d)/sqrt(c)),b*c/(a*d))*sqrt(c)*sqrt(a+b*x^2)*sqrt((c+_
+-- d*x^2)/c)/(b*(-d)^(5/2)*sqrt((a+b*x^2)/a)*sqrt(c+d*x^2))-_
+-- 1/105*a*(b*c-a*d)*(4*b^2*c^2-13*a*b*c*d-15*a^2*d^2)*_
+-- elliptic_f(asin(x*sqrt(-d)/sqrt(c)),b*c/(a*d))*sqrt(c)*_
+-- sqrt((a+b*x^2)/a)*sqrt((c+d*x^2)/c)/(b*(-d)^(5/2)*sqrt(a+_
+-- b*x^2)*sqrt(c+d*x^2))
+--E 544
+
+--S 545 of 994
+--a0:=integrate(t0,x)
+--E 545
+
+--S 546 of 994
+--m0:=a0-r0
+--E 546
+
+--S 547 of 994
+--d0:=D(m0,x)
+--E 547
+
+)clear all
+
+--S 548 of 994
+t0:=(a+b*x^2)^(3/2)*(c+d*x^2)^(1/2)
+--R
+--R
+--R +--------+ +--------+
+--R 2 | 2 | 2
+--R (1) (b x + a)\|b x + a \|d x + c
+--R Type: Expression(Integer)
+--E 548
+
+--S 549 of 994
+--r0:=1/5*b*x*(c+d*x^2)^(3/2)*sqrt(a+b*x^2)/d-2/15*(b*c-3*a*d)*x*_
+-- sqrt(a+b*x^2)*sqrt(c+d*x^2)/d+1/15*(2*b^2*c^2-7*a*b*c*d-3*_
+-- a^2*d^2)*elliptic_e(asin(x*sqrt(-d)/sqrt(c)),b*c/(a*d))*_
+-- sqrt(c)*sqrt(a+b*x^2)*sqrt((c+d*x^2)/c)/(b*(-d)^(3/2)*_
+-- sqrt((a+b*x^2)/a)*sqrt(c+d*x^2))-1/15*a*(b*c-a*d)*(b*c+3*a*d)*_
+-- elliptic_f(asin(x*sqrt(-d)/sqrt(c)),b*c/(a*d))*sqrt(c)*_
+-- sqrt((a+b*x^2)/a)*sqrt((c+d*x^2)/c)/(b*(-d)^(3/2)*sqrt(a+_
+-- b*x^2)*sqrt(c+d*x^2))
+--E 549
+
+--S 550 of 994
+--a0:=integrate(t0,x)
+--E 550
+
+--S 551 of 994
+--m0:=a0-r0
+--E 551
+
+--S 552 of 994
+--d0:=D(m0,x)
+--E 552
+
+)clear all
+
+--S 553 of 994
+t0:=(a+b*x^2)^(1/2)*(c+d*x^2)^(1/2)
+--R
+--R
+--R +--------+ +--------+
+--R | 2 | 2
+--R (1) \|b x + a \|d x + c
+--R Type: Expression(Integer)
+--E 553
+
+--S 554 of 994
+--r0:=1/3*x*sqrt(a+b*x^2)*sqrt(c+d*x^2)+1/3*(b*c+a*d)*_
+-- elliptic_e(asin(x*sqrt(-d)/sqrt(c)),b*c/(a*d))*sqrt(c)*_
+-- sqrt(a+b*x^2)*sqrt((c+d*x^2)/c)/(b*sqrt(-d)*sqrt((a+b*x^2)/a)*_
+-- sqrt(c+d*x^2))+1/3*a*(b*c-a*d)*elliptic_f(asin(x*sqrt(-d)/_
+-- sqrt(c)),b*c/(a*d))*sqrt(c)*sqrt((a+b*x^2)/a)*sqrt((c+d*x^2)/_
+-- c)/(b*sqrt(-d)*sqrt(a+b*x^2)*sqrt(c+d*x^2))
+--E 554
+
+--S 555 of 994
+--a0:=integrate(t0,x)
+--E 555
+
+--S 556 of 994
+--m0:=a0-r0
+--E 556
+
+--S 557 of 994
+--d0:=D(m0,x)
+--E 557
+
+)clear all
+
+--S 558 of 994
+t0:=(c+d*x^2)^(1/2)/(a+b*x^2)^(1/2)
+--R
+--R
+--R +--------+
+--R | 2
+--R \|d x + c
+--R (1) -----------
+--R +--------+
+--R | 2
+--R \|b x + a
+--R Type: Expression(Integer)
+--E 558
+
+--S 559 of 994
+--r0:=elliptic_e(asin(x*sqrt(-b)/sqrt(a)),a*d/(b*c))*sqrt(a)*_
+-- sqrt((a+b*x^2)/a)*sqrt(c+d*x^2)/(sqrt(-b)*sqrt(a+b*x^2)*sqrt((c+d*x^2)/c))
+--E 559
+
+--S 560 of 994
+--a0:=integrate(t0,x)
+--E 560
+
+--S 561 of 994
+--m0:=a0-r0
+--E 561
+
+--S 562 of 994
+--d0:=D(m0,x)
+--E 562
+
+)clear all
+
+--S 563 of 994
+t0:=(c+d*x^2)^(1/2)/(a+b*x^2)^(3/2)
+--R
+--R
+--R +--------+
+--R | 2
+--R \|d x + c
+--R (1) ---------------------
+--R +--------+
+--R 2 | 2
+--R (b x + a)\|b x + a
+--R Type: Expression(Integer)
+--E 563
+
+--S 564 of 994
+--r0:=x*sqrt(c+d*x^2)/(a*sqrt(a+b*x^2))+elliptic_e(asin(x*sqrt(-d)/_
+-- sqrt(c)),b*c/(a*d))*sqrt(c)*sqrt(-d)*sqrt(a+b*x^2)*sqrt((c+_
+-- d*x^2)/c)/(a*b*sqrt((a+b*x^2)/a)*sqrt(c+d*x^2))-_
+-- elliptic_f(asin(x*sqrt(-d)/sqrt(c)),b*c/(a*d))*sqrt(c)*_
+-- sqrt(-d)*sqrt((a+b*x^2)/a)*sqrt((c+d*x^2)/c)/(b*sqrt(a+b*x^2)*_
+-- sqrt(c+d*x^2))
+--E 564
+
+--S 565 of 994
+--a0:=integrate(t0,x)
+--E 565
+
+--S 566 of 994
+--m0:=a0-r0
+--E 566
+
+--S 567 of 994
+--d0:=D(m0,x)
+--E 567
+
+)clear all
+
+--S 568 of 994
+t0:=(c+d*x^2)^(1/2)/(a+b*x^2)^(5/2)
+--R
+--R
+--R +--------+
+--R | 2
+--R \|d x + c
+--R (1) --------------------------------
+--R +--------+
+--R 2 4 2 2 | 2
+--R (b x + 2a b x + a )\|b x + a
+--R Type: Expression(Integer)
+--E 568
+
+--S 569 of 994
+--r0:=1/3*x*sqrt(c+d*x^2)/(a*(a+b*x^2)^(3/2))+1/3*(2*b*c-a*d)*x*_
+-- sqrt(c+d*x^2)/(a^2*(b*c-a*d)*sqrt(a+b*x^2))+1/3*(2*b*c-a*d)*_
+-- elliptic_e(asin(x*sqrt(-d)/sqrt(c)),b*c/(a*d))*sqrt(c)*_
+-- sqrt(-d)*sqrt(a+b*x^2)*sqrt((c+d*x^2)/c)/(a^2*b*(b*c-a*d)*_
+-- sqrt((a+b*x^2)/a)*sqrt(c+d*x^2))-1/3*elliptic_f(asin(x*_
+-- sqrt(-d)/sqrt(c)),b*c/(a*d))*sqrt(c)*sqrt(-d)*sqrt((a+b*x^2)/a)*_
+-- sqrt((c+d*x^2)/c)/(a*b*sqrt(a+b*x^2)*sqrt(c+d*x^2))
+--E 569
+
+--S 570 of 994
+--a0:=integrate(t0,x)
+--E 570
+
+--S 571 of 994
+--m0:=a0-r0
+--E 571
+
+--S 572 of 994
+--d0:=D(m0,x)
+--E 572
+
+)clear all
+
+--S 573 of 994
+t0:=(c+d*x^2)^(1/2)/(a+b*x^2)^(7/2)
+--R
+--R
+--R +--------+
+--R | 2
+--R \|d x + c
+--R (1) ------------------------------------------
+--R +--------+
+--R 3 6 2 4 2 2 3 | 2
+--R (b x + 3a b x + 3a b x + a )\|b x + a
+--R Type: Expression(Integer)
+--E 573
+
+--S 574 of 994
+--r0:=1/5*x*sqrt(c+d*x^2)/(a*(a+b*x^2)^(5/2))+1/15*(4*b*c-3*a*d)*x*_
+-- sqrt(c+d*x^2)/(a^2*(b*c-a*d)*(a+b*x^2)^(3/2))+1/15*(8*b^2*c^2-_
+-- 13*a*b*c*d+3*a^2*d^2)*x*sqrt(c+d*x^2)/(a^3*(b*c-a*d)^2*sqrt(a+_
+-- b*x^2))+1/15*(8*b^2*c^2-13*a*b*c*d+3*a^2*d^2)*elliptic_e(_
+-- asin(x*sqrt(-d)/sqrt(c)),b*c/(a*d))*sqrt(c)*sqrt(-d)*sqrt(a+_
+-- b*x^2)*sqrt((c+d*x^2)/c)/(a^3*b*(b*c-a*d)^2*sqrt((a+b*x^2)/a)*_
+-- sqrt(c+d*x^2))-1/15*(4*b*c-3*a*d)*elliptic_f(asin(x*sqrt(-d)/_
+-- sqrt(c)),b*c/(a*d))*sqrt(c)*sqrt(-d)*sqrt((a+b*x^2)/a)*_
+-- sqrt((c+d*x^2)/c)/(a^2*b*(b*c-a*d)*sqrt(a+b*x^2)*sqrt(c+d*x^2))
+--E 574
+
+--S 575 of 994
+--a0:=integrate(t0,x)
+--E 575
+
+--S 576 of 994
+--m0:=a0-r0
+--E 576
+
+--S 577 of 994
+--d0:=D(m0,x)
+--E 577
+
+)clear all
+
+--S 578 of 994
+t0:=(a+b*x^2)^(3/2)*(c+d*x^2)^(3/2)
+--R
+--R
+--R +--------+ +--------+
+--R 4 2 | 2 | 2
+--R (1) (b d x + (a d + b c)x + a c)\|b x + a \|d x + c
+--R Type: Expression(Integer)
+--E 578
+
+--S 579 of 994
+--r0:=2/35*(4*b*c-a*d)*x*(a+b*x^2)^(3/2)*sqrt(c+d*x^2)/b+1/7*d*x*(a+_
+-- b*x^2)^(5/2)*sqrt(c+d*x^2)/b+1/35*(9*a*c+b*c^2/d-2*a^2*d/b)*_
+-- x*sqrt(a+b*x^2)*sqrt(c+d*x^2)+2/35*(b*c+a*d)*(b^2*c^2-6*a*b*c*d+_
+-- a^2*d^2)*elliptic_e(asin(x*sqrt(-d)/sqrt(c)),b*c/(a*d))*sqrt(c)*_
+-- sqrt(a+b*x^2)*sqrt((c+d*x^2)/c)/(b^2*(-d)^(3/2)*sqrt((a+b*x^2)/a)*_
+-- sqrt(c+d*x^2))-1/35*a*(b*c-a*d)*(b^2*c^2+9*a*b*c*d-2*a^2*d^2)*_
+-- elliptic_f(asin(x*sqrt(-d)/sqrt(c)),b*c/(a*d))*sqrt(c)*_
+-- sqrt((a+b*x^2)/a)*sqrt((c+d*x^2)/c)/(b^2*(-d)^(3/2)*_
+-- sqrt(a+b*x^2)*sqrt(c+d*x^2))
+--E 579
+
+--S 580 of 994
+--a0:=integrate(t0,x)
+--E 580
+
+--S 581 of 994
+--m0:=a0-r0
+--E 581
+
+--S 582 of 994
+--d0:=D(m0,x)
+--E 582
+
+)clear all
+
+--S 583 of 994
+t0:=(a+b*x^2)^(1/2)*(c+d*x^2)^(3/2)
+--R
+--R
+--R +--------+ +--------+
+--R 2 | 2 | 2
+--R (1) (d x + c)\|b x + a \|d x + c
+--R Type: Expression(Integer)
+--E 583
+
+--S 584 of 994
+--r0:=1/5*d*x*(a+b*x^2)^(3/2)*sqrt(c+d*x^2)/b+2/15*(3*b*c-a*d)*x*_
+-- sqrt(a+b*x^2)*sqrt(c+d*x^2)/b+1/15*(3*b^2*c^2+7*a*b*c*d-2*a^2*_
+-- d^2)*elliptic_e(asin(x*sqrt(-d)/sqrt(c)),b*c/(a*d))*sqrt(c)*_
+-- sqrt(a+b*x^2)*sqrt((c+d*x^2)/c)/(b^2*sqrt(-d)*sqrt((a+b*x^2)/a)*_
+-- sqrt(c+d*x^2))+2/15*a*(b*c-a*d)*(3*b*c-a*d)*elliptic_f(asin(x*_
+-- sqrt(-d)/sqrt(c)),b*c/(a*d))*sqrt(c)*sqrt((a+b*x^2)/a)*_
+-- sqrt((c+d*x^2)/c)/(b^2*sqrt(-d)*sqrt(a+b*x^2)*sqrt(c+d*x^2))
+--E 584
+
+--S 585 of 994
+--a0:=integrate(t0,x)
+--E 585
+
+--S 586 of 994
+--m0:=a0-r0
+--E 586
+
+--S 587 of 994
+--d0:=D(m0,x)
+--E 587
+
+)clear all
+
+--S 588 of 994
+t0:=(c+d*x^2)^(3/2)/(a+b*x^2)^(1/2)
+--R
+--R
+--R +--------+
+--R 2 | 2
+--R (d x + c)\|d x + c
+--R (1) ---------------------
+--R +--------+
+--R | 2
+--R \|b x + a
+--R Type: Expression(Integer)
+--E 588
+
+--S 589 of 994
+--r0:=1/3*d*x*sqrt(a+b*x^2)*sqrt(c+d*x^2)/b-2/3*(2*b*c-a*d)*_
+-- elliptic_e(asin(x*sqrt(-d)/sqrt(c)),b*c/(a*d))*sqrt(c)*sqrt(-d)*_
+-- sqrt(a+b*x^2)*sqrt((c+d*x^2)/c)/(b^2*sqrt((a+b*x^2)/a)*sqrt(c+_
+-- d*x^2))+1/3*(3*b*c-2*a*d)*(b*c-a*d)*elliptic_f(asin(x*sqrt(-d)/_
+-- sqrt(c)),b*c/(a*d))*sqrt(c)*sqrt((a+b*x^2)/a)*sqrt((c+d*x^2)/c)/_
+-- (b^2*sqrt(-d)*sqrt(a+b*x^2)*sqrt(c+d*x^2))
+--E 589
+
+--S 590 of 994
+--a0:=integrate(t0,x)
+--E 590
+
+--S 591 of 994
+--m0:=a0-r0
+--E 591
+
+--S 592 of 994
+--d0:=D(m0,x)
+--E 592
+
+)clear all
+
+--S 593 of 994
+t0:=(c+d*x^2)^(3/2)/(a+b*x^2)^(3/2)
+--R
+--R
+--R +--------+
+--R 2 | 2
+--R (d x + c)\|d x + c
+--R (1) ---------------------
+--R +--------+
+--R 2 | 2
+--R (b x + a)\|b x + a
+--R Type: Expression(Integer)
+--E 593
+
+--S 594 of 994
+--r0:=(b*c-a*d)*x*sqrt(c+d*x^2)/(a*b*sqrt(a+b*x^2))+(b*c-2*a*d)*_
+-- elliptic_e(asin(x*sqrt(-d)/sqrt(c)),b*c/(a*d))*sqrt(c)*sqrt(-d)*_
+-- sqrt(a+b*x^2)*sqrt((c+d*x^2)/c)/(a*b^2*sqrt((a+b*x^2)/a)*_
+-- sqrt(c+d*x^2))-2*(b*c-a*d)*elliptic_f(asin(x*sqrt(-d)/sqrt(c)),_
+-- b*c/(a*d))*sqrt(c)*sqrt(-d)*sqrt((a+b*x^2)/a)*sqrt((c+d*x^2)/c)/_
+-- (b^2*sqrt(a+b*x^2)*sqrt(c+d*x^2))
+--E 594
+
+--S 595 of 994
+--a0:=integrate(t0,x)
+--E 595
+
+--S 596 of 994
+--m0:=a0-r0
+--E 596
+
+--S 597 of 994
+--d0:=D(m0,x)
+--E 597
+
+)clear all
+
+--S 598 of 994
+t0:=(c+d*x^2)^(3/2)/(a+b*x^2)^(5/2)
+--R
+--R
+--R +--------+
+--R 2 | 2
+--R (d x + c)\|d x + c
+--R (1) --------------------------------
+--R +--------+
+--R 2 4 2 2 | 2
+--R (b x + 2a b x + a )\|b x + a
+--R Type: Expression(Integer)
+--E 598
+
+--S 599 of 994
+--r0:=1/3*(b*c-a*d)*x*sqrt(c+d*x^2)/(a*b*(a+b*x^2)^(3/2))+2/3*(b*c+a*d)*_
+-- x*sqrt(c+d*x^2)/(a^2*b*sqrt(a+b*x^2))+2/3*(b*c+a*d)*_
+-- elliptic_e(asin(x*sqrt(-d)/sqrt(c)),b*c/(a*d))*sqrt(c)*_
+-- sqrt(-d)*sqrt(a+b*x^2)*sqrt((c+d*x^2)/c)/(a^2*b^2*sqrt((a+_
+-- b*x^2)/a)*sqrt(c+d*x^2))-1/3*(b*c+2*a*d)*elliptic_f(asin(x*_
+-- sqrt(-d)/sqrt(c)),b*c/(a*d))*sqrt(c)*sqrt(-d)*sqrt((a+b*x^2)/a)*_
+-- sqrt((c+d*x^2)/c)/(a*b^2*sqrt(a+b*x^2)*sqrt(c+d*x^2))
+--E 599
+
+--S 600 of 994
+--a0:=integrate(t0,x)
+--E 600
+
+--S 601 of 994
+--m0:=a0-r0
+--E 601
+
+--S 602 of 994
+--d0:=D(m0,x)
+--E 602
+
+)clear all
+
+--S 603 of 994
+t0:=(c+d*x^2)^(3/2)/(a+b*x^2)^(7/2)
+--R
+--R
+--R +--------+
+--R 2 | 2
+--R (d x + c)\|d x + c
+--R (1) ------------------------------------------
+--R +--------+
+--R 3 6 2 4 2 2 3 | 2
+--R (b x + 3a b x + 3a b x + a )\|b x + a
+--R Type: Expression(Integer)
+--E 603
+
+--S 604 of 994
+--r0:=1/5*(b*c-a*d)*x*sqrt(c+d*x^2)/(a*b*(a+b*x^2)^(5/2))+2/15*(2*b*c+_
+-- a*d)*x*sqrt(c+d*x^2)/(a^2*b*(a+b*x^2)^(3/2))+1/15*(8*b^2*c^2-_
+-- 3*a*b*c*d-2*a^2*d^2)*x*sqrt(c+d*x^2)/(a^3*b*(b*c-a*d)*sqrt(a+_
+-- b*x^2))+1/15*(8*b^2*c^2-3*a*b*c*d-2*a^2*d^2)*elliptic_e(asin(x*_
+-- sqrt(-d)/sqrt(c)),b*c/(a*d))*sqrt(c)*sqrt(-d)*sqrt(a+b*x^2)*_
+-- sqrt((c+d*x^2)/c)/(a^3*b^2*(b*c-a*d)*sqrt((a+b*x^2)/a)*sqrt(c+_
+-- d*x^2))-2/15*(2*b*c+a*d)*elliptic_f(asin(x*sqrt(-d)/sqrt(c)),_
+-- b*c/(a*d))*sqrt(c)*sqrt(-d)*sqrt((a+b*x^2)/a)*sqrt((c+d*x^2)/c)/_
+-- (a^2*b^2*sqrt(a+b*x^2)*sqrt(c+d*x^2))
+--E 604
+
+--S 605 of 994
+--a0:=integrate(t0,x)
+--E 605
+
+--S 606 of 994
+--m0:=a0-r0
+--E 606
+
+--S 607 of 994
+--d0:=D(m0,x)
+--E 607
+
+)clear all
+
+--S 608 of 994
+t0:=sqrt(2+b*x^2)*sqrt(3+d*x^2)
+--R
+--R
+--R +--------+ +--------+
+--R | 2 | 2
+--R (1) \|b x + 2 \|d x + 3
+--R Type: Expression(Integer)
+--E 608
+
+--S 609 of 994
+--r0:=1/3*(3*b+2*d)*elliptic_e(asin(x*sqrt(-d)/sqrt(3)),3/2*b/d)*_
+-- sqrt(2)/(b*sqrt(-d))+1/3*(3*b-2*d)*elliptic_f(asin(x*sqrt(-d)/_
+-- sqrt(3)),3/2*b/d)*sqrt(2)/(b*sqrt(-d))+1/3*x*sqrt(2+b*x^2)*sqrt(3+d*x^2)
+--E 609
+
+--S 610 of 994
+--a0:=integrate(t0,x)
+--E 610
+
+--S 611 of 994
+--m0:=a0-r0
+--E 611
+
+--S 612 of 994
+--d0:=D(m0,x)
+--E 612
+
+)clear all
+
+--S 613 of 994
+t0:=sqrt(a+b*x^2)*sqrt(c+d*x^2)
+--R
+--R
+--R +--------+ +--------+
+--R | 2 | 2
+--R (1) \|b x + a \|d x + c
+--R Type: Expression(Integer)
+--E 613
+
+--S 614 of 994
+--r0:=1/3*x*sqrt(a+b*x^2)*sqrt(c+d*x^2)+1/3*(b*c+a*d)*_
+-- elliptic_e(asin(x*sqrt(-d)/sqrt(c)),b*c/(a*d))*sqrt(c)*_
+-- sqrt(a+b*x^2)*sqrt((c+d*x^2)/c)/(b*sqrt(-d)*sqrt((a+b*x^2)/a)*_
+-- sqrt(c+d*x^2))+1/3*a*(b*c-a*d)*elliptic_f(asin(x*sqrt(-d)/_
+-- sqrt(c)),b*c/(a*d))*sqrt(c)*sqrt((a+b*x^2)/a)*sqrt((c+d*x^2)/c)/_
+-- (b*sqrt(-d)*sqrt(a+b*x^2)*sqrt(c+d*x^2))
+--E 614
+
+--S 615 of 994
+--a0:=integrate(t0,x)
+--E 615
+
+--S 616 of 994
+--m0:=a0-r0
+--E 616
+
+--S 617 of 994
+--d0:=D(m0,x)
+--E 617
+
+)clear all
+
+--S 618 of 994
+t0:=sqrt(3-6*x^2)*sqrt(2+4*x^2)
+--R
+--R
+--R +---------+ +-------+
+--R | 2 | 2
+--R (1) \|- 6x + 3 \|4x + 2
+--R Type: Expression(Integer)
+--E 618
+
+--S 619 of 994
+--r0:=2*elliptic_f(asin(x*sqrt(2)),-1)/sqrt(3)+x*sqrt(2/3)*_
+-- sqrt(1-2*x^2)*sqrt(1+2*x^2)
+--E 619
+
+--S 620 of 994
+--a0:=integrate(t0,x)
+--E 620
+
+--S 621 of 994
+--m0:=a0-r0
+--E 621
+
+--S 622 of 994
+--d0:=D(m0,x)
+--E 622
+
+)clear all
+
+--S 623 of 994
+t0:=sqrt(2+4*x^2)*sqrt(3+6*x^2)
+--R
+--R
+--R +-------+ +-------+
+--R | 2 | 2
+--R (1) \|4x + 2 \|6x + 3
+--R Type: Expression(Integer)
+--E 623
+
+--S 624 of 994
+r0:=2*x^3*sqrt(2/3)+x*sqrt(6)
+--R
+--R
+--R +-+
+--R 2\|2 3 +-+
+--R (2) ----- x + \|6 x
+--R +-+
+--R \|3
+--R Type: Polynomial(AlgebraicNumber)
+--E 624
+
+--S 625 of 994
+a0:=integrate(t0,x)
+--R
+--R
+--R +-------+ +-------+
+--R 3 | 2 | 2
+--R (2x + 3x)\|4x + 2 \|6x + 3
+--R (3) ------------------------------
+--R 2
+--R 6x + 3
+--R Type: Union(Expression(Integer),...)
+--E 625
+
+--S 626 of 994
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +-------+ +-------+
+--R 3 +-+ | 2 | 2 3 +-+ +-+
+--R (2x + 3x)\|3 \|4x + 2 \|6x + 3 + (- 6x - 3x)\|3 \|6
+--R +
+--R 5 3 +-+
+--R (- 12x - 6x )\|2
+--R /
+--R 2 +-+
+--R (6x + 3)\|3
+--R Type: Expression(Integer)
+--E 626
+
+--S 627 of 994
+d0:=D(m0,x)
+--R
+--R
+--R +-------+ +-------+
+--R +-+ 2 +-+ +-+ | 2 | 2 4 2
+--R (- \|6 - 2x \|2 \|3 )\|4x + 2 \|6x + 3 + 24x + 24x + 6
+--R (5) ------------------------------------------------------------
+--R +-------+ +-------+
+--R | 2 | 2
+--R \|4x + 2 \|6x + 3
+--R Type: Expression(Integer)
+--E 627
+
+)clear all
+
+--S 628 of 994
+t0:=(a+b*x^2)^(7/2)/(c+d*x^2)^(1/2)
+--R
+--R
+--R +--------+
+--R 3 6 2 4 2 2 3 | 2
+--R (b x + 3a b x + 3a b x + a )\|b x + a
+--R (1) ------------------------------------------
+--R +--------+
+--R | 2
+--R \|d x + c
+--R Type: Expression(Integer)
+--E 628
+
+--S 629 of 994
+--r0:=-6/35*b*(b*c-2*a*d)*x*(a+b*x^2)^(3/2)*sqrt(c+d*x^2)/d^2+1/7*b*_
+-- x*(a+b*x^2)^(5/2)*sqrt(c+d*x^2)/d+1/105*b*(24*b^2*c^2-71*a*b*_
+-- c*d+71*a^2*d^2)*x*sqrt(a+b*x^2)*sqrt(c+d*x^2)/d^3+8/105*(b*c-_
+-- 2*a*d)*(6*b^2*c^2-11*a*b*c*d+11*a^2*d^2)*elliptic_e(asin(x*_
+-- sqrt(-d)/sqrt(c)),b*c/(a*d))*sqrt(c)*sqrt(a+b*x^2)*sqrt((c+d*_
+-- x^2)/c)/((-d)^(7/2)*sqrt((a+b*x^2)/a)*sqrt(c+d*x^2))-1/105*_
+-- a*(b*c-a*d)*(24*b^2*c^2-71*a*b*c*d+71*a^2*d^2)*elliptic_f(_
+-- asin(x*sqrt(-d)/sqrt(c)),b*c/(a*d))*sqrt(c)*sqrt((a+b*x^2)/a)*_
+-- sqrt((c+d*x^2)/c)/((-d)^(7/2)*sqrt(a+b*x^2)*sqrt(c+d*x^2))
+--E 629
+
+--S 630 of 994
+--a0:=integrate(t0,x)
+--E 630
+
+--S 631 of 994
+--m0:=a0-r0
+--E 631
+
+--S 632 of 994
+--d0:=D(m0,x)
+--E 632
+
+)clear all
+
+--S 633 of 994
+t0:=(a+b*x^2)^(5/2)/(c+d*x^2)^(1/2)
+--R
+--R
+--R +--------+
+--R 2 4 2 2 | 2
+--R (b x + 2a b x + a )\|b x + a
+--R (1) --------------------------------
+--R +--------+
+--R | 2
+--R \|d x + c
+--R Type: Expression(Integer)
+--E 633
+
+--S 634 of 994
+--r0:=1/5*b*x*(a+b*x^2)^(3/2)*sqrt(c+d*x^2)/d-4/15*b*(b*c-2*a*d)*x*_
+-- sqrt(a+b*x^2)*sqrt(c+d*x^2)/d^2+1/15*(8*b^2*c^2-23*a*b*c*d+23*_
+-- a^2*d^2)*elliptic_e(asin(x*sqrt(-d)/sqrt(c)),b*c/(a*d))*_
+-- sqrt(c)*sqrt(a+b*x^2)*sqrt((c+d*x^2)/c)/((-d)^(5/2)*_
+-- sqrt((a+b*x^2)/a)*sqrt(c+d*x^2))-4/15*a*(b*c-2*a*d)*(b*c-a*d)*_
+-- elliptic_f(asin(x*sqrt(-d)/sqrt(c)),b*c/(a*d))*sqrt(c)*_
+-- sqrt((a+b*x^2)/a)*sqrt((c+d*x^2)/c)/((-d)^(5/2)*sqrt(a+b*x^2)*_
+-- sqrt(c+d*x^2))
+--E 634
+
+--S 635 of 994
+--a0:=integrate(t0,x)
+--E 635
+
+--S 636 of 994
+--m0:=a0-r0
+--E 636
+
+--S 637 of 994
+--d0:=D(m0,x)
+--E 637
+
+)clear all
+
+--S 638 of 994
+t0:=(a+b*x^2)^(3/2)/(c+d*x^2)^(1/2)
+--R
+--R
+--R +--------+
+--R 2 | 2
+--R (b x + a)\|b x + a
+--R (1) ---------------------
+--R +--------+
+--R | 2
+--R \|d x + c
+--R Type: Expression(Integer)
+--E 638
+
+--S 639 of 994
+--r0:=1/3*b*x*sqrt(a+b*x^2)*sqrt(c+d*x^2)/d+2/3*(b*c-2*a*d)*_
+-- elliptic_e(asin(x*sqrt(-d)/sqrt(c)),b*c/(a*d))*sqrt(c)*_
+-- sqrt(a+b*x^2)*sqrt((c+d*x^2)/c)/((-d)^(3/2)*sqrt((a+b*x^2)/a)*_
+-- sqrt(c+d*x^2))-1/3*a*(b*c-a*d)*elliptic_f(asin(x*sqrt(-d)/_
+-- sqrt(c)),b*c/(a*d))*sqrt(c)*sqrt((a+b*x^2)/a)*sqrt((c+d*x^2)/c)/_
+-- ((-d)^(3/2)*sqrt(a+b*x^2)*sqrt(c+d*x^2))
+--E 639
+
+--S 640 of 994
+--a0:=integrate(t0,x)
+--E 640
+
+--S 641 of 994
+--m0:=a0-r0
+--E 641
+
+--S 642 of 994
+--d0:=D(m0,x)
+--E 642
+
+)clear all
+
+--S 643 of 994
+t0:=(a+b*x^2)^(1/2)/(c+d*x^2)^(1/2)
+--R
+--R
+--R +--------+
+--R | 2
+--R \|b x + a
+--R (1) -----------
+--R +--------+
+--R | 2
+--R \|d x + c
+--R Type: Expression(Integer)
+--E 643
+
+--S 644 of 994
+--r0:=elliptic_e(asin(x*sqrt(-d)/sqrt(c)),b*c/(a*d))*sqrt(c)*_
+-- sqrt(a+b*x^2)*sqrt((c+d*x^2)/c)/(sqrt(-d)*sqrt((a+b*x^2)/a)*sqrt(c+d*x^2))
+--E 644
+
+--S 645 of 994
+--a0:=integrate(t0,x)
+--E 645
+
+--S 646 of 994
+--m0:=a0-r0
+--E 646
+
+--S 647 of 994
+--d0:=D(m0,x)
+--E 647
+
+)clear all
+
+--S 648 of 994
+t0:=1/((a+b*x^2)^(1/2)*(c+d*x^2)^(1/2))
+--R
+--R
+--R 1
+--R (1) ----------------------
+--R +--------+ +--------+
+--R | 2 | 2
+--R \|b x + a \|d x + c
+--R Type: Expression(Integer)
+--E 648
+
+--S 649 of 994
+--r0:=elliptic_f(asin(x*sqrt(-d)/sqrt(c)),b*c/(a*d))*sqrt(c)*_
+-- sqrt((a+b*x^2)/a)*sqrt((c+d*x^2)/c)/(sqrt(-d)*sqrt(a+b*x^2)*sqrt(c+d*x^2))
+--E 649
+
+--S 650 of 994
+--a0:=integrate(t0,x)
+--E 650
+
+--S 651 of 994
+--m0:=a0-r0
+--E 651
+
+--S 652 of 994
+--d0:=D(m0,x)
+--E 652
+
+)clear all
+
+--S 653 of 994
+t0:=1/((a+b*x^2)^(3/2)*(c+d*x^2)^(1/2))
+--R
+--R
+--R 1
+--R (1) --------------------------------
+--R +--------+ +--------+
+--R 2 | 2 | 2
+--R (b x + a)\|b x + a \|d x + c
+--R Type: Expression(Integer)
+--E 653
+
+--S 654 of 994
+--r0:=b*x*sqrt(c+d*x^2)/(a*(b*c-a*d)*sqrt(a+b*x^2))+elliptic_e(_
+-- asin(x*sqrt(-d)/sqrt(c)),b*c/(a*d))*sqrt(c)*sqrt(-d)*_
+-- sqrt(a+b*x^2)*sqrt((c+d*x^2)/c)/(a*(b*c-a*d)*sqrt((a+b*x^2)/a)*_
+-- sqrt(c+d*x^2))
+--E 654
+
+--S 655 of 994
+--a0:=integrate(t0,x)
+--E 655
+
+--S 656 of 994
+--m0:=a0-r0
+--E 656
+
+--S 657 of 994
+--d0:=D(m0,x)
+--E 657
+
+)clear all
+
+--S 658 of 994
+t0:=1/((a+b*x^2)^(5/2)*(c+d*x^2)^(1/2))
+--R
+--R
+--R 1
+--R (1) -------------------------------------------
+--R +--------+ +--------+
+--R 2 4 2 2 | 2 | 2
+--R (b x + 2a b x + a )\|b x + a \|d x + c
+--R Type: Expression(Integer)
+--E 658
+
+--S 659 of 994
+--r0:=1/3*b*x*sqrt(c+d*x^2)/(a*(b*c-a*d)*(a+b*x^2)^(3/2))+2/3*b*_
+-- (b*c-2*a*d)*x*sqrt(c+d*x^2)/(a^2*(b*c-a*d)^2*sqrt(a+b*x^2))+_
+-- 2/3*(b*c-2*a*d)*elliptic_e(asin(x*sqrt(-d)/sqrt(c)),b*c/(a*d))*_
+-- sqrt(c)*sqrt(-d)*sqrt(a+b*x^2)*sqrt((c+d*x^2)/c)/(a^2*(b*c-_
+-- a*d)^2*sqrt((a+b*x^2)/a)*sqrt(c+d*x^2))-1/3*elliptic_f(_
+-- asin(x*sqrt(-d)/sqrt(c)),b*c/(a*d))*sqrt(c)*sqrt(-d)*_
+-- sqrt((a+b*x^2)/a)*sqrt((c+d*x^2)/c)/(a*(b*c-a*d)*_
+-- sqrt(a+b*x^2)*sqrt(c+d*x^2))
+--E 659
+
+--S 660 of 994
+--a0:=integrate(t0,x)
+--E 660
+
+--S 661 of 994
+--m0:=a0-r0
+--E 661
+
+--S 662 of 994
+--d0:=D(m0,x)
+--E 662
+
+)clear all
+
+--S 663 of 994
+t0:=1/((a+b*x^2)^(7/2)*(c+d*x^2)^(1/2))
+--R
+--R
+--R 1
+--R (1) -----------------------------------------------------
+--R +--------+ +--------+
+--R 3 6 2 4 2 2 3 | 2 | 2
+--R (b x + 3a b x + 3a b x + a )\|b x + a \|d x + c
+--R Type: Expression(Integer)
+--E 663
+
+--S 664 of 994
+--r0:=1/5*b*x*sqrt(c+d*x^2)/(a*(b*c-a*d)*(a+b*x^2)^(5/2))+4/15*b*_
+-- (b*c-2*a*d)*x*sqrt(c+d*x^2)/(a^2*(b*c-a*d)^2*(a+b*x^2)^(3/2))+_
+-- 1/15*b*(8*b^2*c^2-23*a*b*c*d+23*a^2*d^2)*x*sqrt(c+d*x^2)/_
+-- (a^3*(b*c-a*d)^3*sqrt(a+b*x^2))+1/15*(8*b^2*c^2-23*a*b*c*d+_
+-- 23*a^2*d^2)*elliptic_e(asin(x*sqrt(-d)/sqrt(c)),b*c/(a*d))*_
+-- sqrt(c)*sqrt(-d)*sqrt(a+b*x^2)*sqrt((c+d*x^2)/c)/(a^3*(b*c-_
+-- a*d)^3*sqrt((a+b*x^2)/a)*sqrt(c+d*x^2))-4/15*(b*c-2*a*d)*_
+-- elliptic_f(asin(x*sqrt(-d)/sqrt(c)),b*c/(a*d))*sqrt(c)*_
+-- sqrt(-d)*sqrt((a+b*x^2)/a)*sqrt((c+d*x^2)/c)/(a^2*(b*c-a*d)^2*_
+-- sqrt(a+b*x^2)*sqrt(c+d*x^2))
+--E 664
+
+--S 665 of 994
+--a0:=integrate(t0,x)
+--E 665
+
+--S 666 of 994
+--m0:=a0-r0
+--E 666
+
+--S 667 of 994
+--d0:=D(m0,x)
+--E 667
+
+)clear all
+
+--S 668 of 994
+t0:=(a+b*x^2)^(7/2)/(c+d*x^2)^(3/2)
+--R
+--R
+--R +--------+
+--R 3 6 2 4 2 2 3 | 2
+--R (b x + 3a b x + 3a b x + a )\|b x + a
+--R (1) ------------------------------------------
+--R +--------+
+--R 2 | 2
+--R (d x + c)\|d x + c
+--R Type: Expression(Integer)
+--E 668
+
+--S 669 of 994
+--r0:=-(b*c-a*d)*x*(a+b*x^2)^(5/2)/(c*d*sqrt(c+d*x^2))+1/5*b*(6*b*c-_
+-- 5*a*d)*x*(a+b*x^2)^(3/2)*sqrt(c+d*x^2)/(c*d^2)-1/15*b*(24*b^2*_
+-- c^2-43*a*b*c*d+15*a^2*d^2)*x*sqrt(a+b*x^2)*sqrt(c+d*x^2)/_
+-- (c*d^3)-1/15*(48*b^3*c^3-128*a*b^2*c^2*d+103*a^2*b*c*d^2-_
+-- 15*a^3*d^3)*elliptic_e(asin(x*sqrt(-d)/sqrt(c)),b*c/(a*d))*_
+-- sqrt(a+b*x^2)*sqrt((c+d*x^2)/c)/((-d)^(7/2)*sqrt(c)*_
+-- sqrt((a+b*x^2)/a)*sqrt(c+d*x^2))+1/15*a*(b*c-a*d)*(24*b^2*_
+-- c^2-43*a*b*c*d+15*a^2*d^2)*elliptic_f(asin(x*sqrt(-d)/_
+-- sqrt(c)),b*c/(a*d))*sqrt((a+b*x^2)/a)*sqrt((c+d*x^2)/c)/_
+-- ((-d)^(7/2)*sqrt(c)*sqrt(a+b*x^2)*sqrt(c+d*x^2))
+--E 669
+
+--S 670 of 994
+--a0:=integrate(t0,x)
+--E 670
+
+--S 671 of 994
+--m0:=a0-r0
+--E 671
+
+--S 672 of 994
+--d0:=D(m0,x)
+--E 672
+
+)clear all
+
+--S 673 of 994
+t0:=(a+b*x^2)^(5/2)/(c+d*x^2)^(3/2)
+--R
+--R
+--R +--------+
+--R 2 4 2 2 | 2
+--R (b x + 2a b x + a )\|b x + a
+--R (1) --------------------------------
+--R +--------+
+--R 2 | 2
+--R (d x + c)\|d x + c
+--R Type: Expression(Integer)
+--E 673
+
+--S 674 of 994
+--r0:=-(b*c-a*d)*x*(a+b*x^2)^(3/2)/(c*d*sqrt(c+d*x^2))+1/3*b*_
+-- (4*b*c-3*a*d)*x*sqrt(a+b*x^2)*sqrt(c+d*x^2)/(c*d^2)-1/3*_
+-- (8*b^2*c^2-13*a*b*c*d+3*a^2*d^2)*elliptic_e(asin(x*sqrt(-d)/_
+-- sqrt(c)),b*c/(a*d))*sqrt(a+b*x^2)*sqrt((c+d*x^2)/c)/((-d)^(5/2)*_
+-- sqrt(c)*sqrt((a+b*x^2)/a)*sqrt(c+d*x^2))+1/3*a*(4*b*c-3*a*d)*_
+-- (b*c-a*d)*elliptic_f(asin(x*sqrt(-d)/sqrt(c)),b*c/(a*d))*_
+-- sqrt((a+b*x^2)/a)*sqrt((c+d*x^2)/c)/((-d)^(5/2)*sqrt(c)*_
+-- sqrt(a+b*x^2)*sqrt(c+d*x^2))
+--E 674
+
+--S 675 of 994
+--a0:=integrate(t0,x)
+--E 675
+
+--S 676 of 994
+--m0:=a0-r0
+--E 676
+
+--S 677 of 994
+--d0:=D(m0,x)
+--E 677
+
+)clear all
+
+--S 678 of 994
+t0:=(a+b*x^2)^(3/2)/(c+d*x^2)^(3/2)
+--R
+--R
+--R +--------+
+--R 2 | 2
+--R (b x + a)\|b x + a
+--R (1) ---------------------
+--R +--------+
+--R 2 | 2
+--R (d x + c)\|d x + c
+--R Type: Expression(Integer)
+--E 678
+
+--S 679 of 994
+--r0:=-(b*c-a*d)*x*sqrt(a+b*x^2)/(c*d*sqrt(c+d*x^2))-(2*b*c-a*d)*_
+-- elliptic_e(asin(x*sqrt(-d)/sqrt(c)),b*c/(a*d))*sqrt(a+b*x^2)*_
+-- sqrt((c+d*x^2)/c)/((-d)^(3/2)*sqrt(c)*sqrt((a+b*x^2)/a)*_
+-- sqrt(c+d*x^2))+a*(b*c-a*d)*elliptic_f(asin(x*sqrt(-d)/sqrt(c)),_
+-- b*c/(a*d))*sqrt((a+b*x^2)/a)*sqrt((c+d*x^2)/c)/((-d)^(3/2)*_
+-- sqrt(c)*sqrt(a+b*x^2)*sqrt(c+d*x^2))
+--E 679
+
+--S 680 of 994
+--a0:=integrate(t0,x)
+--E 680
+
+--S 681 of 994
+--m0:=a0-r0
+--E 681
+
+--S 682 of 994
+--d0:=D(m0,x)
+--E 682
+
+)clear all
+
+--S 683 of 994
+t0:=(a+b*x^2)^(1/2)/(c+d*x^2)^(3/2)
+--R
+--R
+--R +--------+
+--R | 2
+--R \|b x + a
+--R (1) ---------------------
+--R +--------+
+--R 2 | 2
+--R (d x + c)\|d x + c
+--R Type: Expression(Integer)
+--E 683
+
+--S 684 of 994
+--r0:=x*sqrt(a+b*x^2)/(c*sqrt(c+d*x^2))-elliptic_e(asin(x*sqrt(-d)/_
+-- sqrt(c)),b*c/(a*d))*sqrt(a+b*x^2)*sqrt((c+d*x^2)/c)/(sqrt(c)*_
+-- sqrt(-d)*sqrt((a+b*x^2)/a)*sqrt(c+d*x^2))+a*elliptic_f(_
+-- asin(x*sqrt(-d)/sqrt(c)),b*c/(a*d))*sqrt((a+b*x^2)/a)*_
+-- sqrt((c+d*x^2)/c)/(sqrt(c)*sqrt(-d)*sqrt(a+b*x^2)*sqrt(c+d*x^2))
+--E 684
+
+--S 685 of 994
+--a0:=integrate(t0,x)
+--E 685
+
+--S 686 of 994
+--m0:=a0-r0
+--E 686
+
+--S 687 of 994
+--d0:=D(m0,x)
+--E 687
+
+)clear all
+
+--S 688 of 994
+t0:=1/((a+b*x^2)^(1/2)*(c+d*x^2)^(3/2))
+--R
+--R
+--R 1
+--R (1) --------------------------------
+--R +--------+ +--------+
+--R 2 | 2 | 2
+--R (d x + c)\|b x + a \|d x + c
+--R Type: Expression(Integer)
+--E 688
+
+--S 689 of 994
+--r0:=-d*x*sqrt(a+b*x^2)/(c*(b*c-a*d)*sqrt(c+d*x^2))-_
+-- elliptic_e(asin(x*sqrt(-b)/sqrt(a)),a*d/(b*c))*sqrt(a)*_
+-- sqrt(-b)*sqrt((a+b*x^2)/a)*sqrt(c+d*x^2)/(c*(b*c-a*d)*_
+-- sqrt(a+b*x^2)*sqrt((c+d*x^2)/c))
+--E 689
+
+--S 690 of 994
+--a0:=integrate(t0,x)
+--E 690
+
+--S 691 of 994
+--m0:=a0-r0
+--E 691
+
+--S 692 of 994
+--d0:=D(m0,x)
+--E 692
+
+)clear all
+
+--S 693 of 994
+t0:=1/((a+b*x^2)^(3/2)*(c+d*x^2)^(3/2))
+--R
+--R
+--R 1
+--R (1) ----------------------------------------------------
+--R +--------+ +--------+
+--R 4 2 | 2 | 2
+--R (b d x + (a d + b c)x + a c)\|b x + a \|d x + c
+--R Type: Expression(Integer)
+--E 693
+
+--S 694 of 994
+--r0:=b*x/(a*(b*c-a*d)*sqrt(a+b*x^2)*sqrt(c+d*x^2))+d*(b*c+a*d)*x*_
+-- sqrt(a+b*x^2)/(a*c*(b*c-a*d)^2*sqrt(c+d*x^2))+(b*c+a*d)*_
+-- elliptic_e(asin(x*sqrt(-d)/sqrt(c)),b*c/(a*d))*sqrt(-d)*_
+-- sqrt(a+b*x^2)*sqrt((c+d*x^2)/c)/(a*(b*c-a*d)^2*sqrt(c)*_
+-- sqrt((a+b*x^2)/a)*sqrt(c+d*x^2))+elliptic_f(asin(x*sqrt(-d)/_
+-- sqrt(c)),b*c/(a*d))*sqrt(-d)*sqrt((a+b*x^2)/a)*sqrt((c+_
+-- d*x^2)/c)/((b*c-a*d)*sqrt(c)*sqrt(a+b*x^2)*sqrt(c+d*x^2))
+--E 694
+
+--S 695 of 994
+--a0:=integrate(t0,x)
+--E 695
+
+--S 696 of 994
+--m0:=a0-r0
+--E 696
+
+--S 697 of 994
+--d0:=D(m0,x)
+--E 697
+
+)clear all
+
+--S 698 of 994
+t0:=1/((a+b*x^2)^(5/2)*(c+d*x^2)^(3/2))
+--R
+--R
+--R (1)
+--R 1
+--R --------------------------------------------------------------------------
+--R +--------+ +--------+
+--R 2 6 2 4 2 2 2 | 2 | 2
+--R (b d x + (2a b d + b c)x + (a d + 2a b c)x + a c)\|b x + a \|d x + c
+--R Type: Expression(Integer)
+--E 698
+
+--S 699 of 994
+--r0:=1/3*b*x/(a*(b*c-a*d)*(a+b*x^2)^(3/2)*sqrt(c+d*x^2))+2/3*b*(b*c-_
+-- 3*a*d)*x/(a^2*(b*c-a*d)^2*sqrt(a+b*x^2)*sqrt(c+d*x^2))+1/3*_
+-- d*(2*b^2*c^2-7*a*b*c*d-3*a^2*d^2)*x*sqrt(a+b*x^2)/(a^2*c*(b*c-_
+-- a*d)^3*sqrt(c+d*x^2))+1/3*(2*b^2*c^2-7*a*b*c*d-3*a^2*d^2)*_
+-- elliptic_e(asin(x*sqrt(-d)/sqrt(c)),b*c/(a*d))*sqrt(-d)*_
+-- sqrt(a+b*x^2)*sqrt((c+d*x^2)/c)/(a^2*(b*c-a*d)^3*sqrt(c)*_
+-- sqrt((a+b*x^2)/a)*sqrt(c+d*x^2))-1/3*(b*c+3*a*d)*_
+-- elliptic_f(asin(x*sqrt(-d)/sqrt(c)),b*c/(a*d))*sqrt(-d)*_
+-- sqrt((a+b*x^2)/a)*sqrt((c+d*x^2)/c)/(a*(b*c-a*d)^2*sqrt(c)*_
+-- sqrt(a+b*x^2)*sqrt(c+d*x^2))
+--E 699
+
+--S 700 of 994
+--a0:=integrate(t0,x)
+--E 700
+
+--S 701 of 994
+--m0:=a0-r0
+--E 701
+
+--S 702 of 994
+--d0:=D(m0,x)
+--E 702
+
+)clear all
+
+--S 703 of 994
+t0:=1/(sqrt(2+b*x^2)*sqrt(3+d*x^2))
+--R
+--R
+--R 1
+--R (1) ----------------------
+--R +--------+ +--------+
+--R | 2 | 2
+--R \|b x + 2 \|d x + 3
+--R Type: Expression(Integer)
+--E 703
+
+--S 704 of 994
+--r0:=elliptic_f(asin(x*sqrt(-d)/sqrt(3)),3/2*b/d)/(sqrt(2)*sqrt(-d))
+--E 704
+
+--S 705 of 994
+--a0:=integrate(t0,x)
+--E 705
+
+--S 706 of 994
+--m0:=a0-r0
+--E 706
+
+--S 707 of 994
+--d0:=D(m0,x)
+--E 707
+
+)clear all
+
+--S 708 of 994
+t0:=1/(sqrt(a+b*x^2)*sqrt(c+d*x^2))
+--R
+--R
+--R 1
+--R (1) ----------------------
+--R +--------+ +--------+
+--R | 2 | 2
+--R \|b x + a \|d x + c
+--R Type: Expression(Integer)
+--E 708
+
+--S 709 of 994
+--r0:=elliptic_f(asin(x*sqrt(-d)/sqrt(c)),b*c/(a*d))*sqrt(c)*_
+-- sqrt((a+b*x^2)/a)*sqrt((c+d*x^2)/c)/(sqrt(-d)*sqrt(a+b*x^2)*sqrt(c+d*x^2))
+--E 709
+
+--S 710 of 994
+--a0:=integrate(t0,x)
+--E 710
+
+--S 711 of 994
+--m0:=a0-r0
+--E 711
+
+--S 712 of 994
+--d0:=D(m0,x)
+--E 712
+
+)clear all
+
+--S 713 of 994
+t0:=1/(sqrt(4-x^2)*sqrt(c+d*x^2))
+--R
+--R
+--R 1
+--R (1) ----------------------
+--R +--------+ +--------+
+--R | 2 | 2
+--R \|- x + 4 \|d x + c
+--R Type: Expression(Integer)
+--E 713
+
+--S 714 of 994
+--r0:=elliptic_f(asin(1/2*x),-4*d/c)*sqrt((c+d*x^2)/c)/sqrt(c+d*x^2)
+--E 714
+
+--S 715 of 994
+--a0:=integrate(t0,x)
+--E 715
+
+--S 716 of 994
+--m0:=a0-r0
+--E 716
+
+--S 717 of 994
+--d0:=D(m0,x)
+--E 717
+
+)clear all
+
+--S 718 of 994
+t0:=1/(sqrt(4+x^2)*sqrt(c+d*x^2))
+--R
+--R
+--R 1
+--R (1) --------------------
+--R +------+ +--------+
+--R | 2 | 2
+--R \|x + 4 \|d x + c
+--R Type: Expression(Integer)
+--E 718
+
+--S 719 of 994
+--r0:=-%i*elliptic_f(%i*asinh(1/2*x),4*d/c)*sqrt((c+d*x^2)/c)/sqrt(c+d*x^2)
+--E 719
+
+--S 720 of 994
+--a0:=integrate(t0,x)
+--E 720
+
+--S 721 of 994
+--m0:=a0-r0
+--E 721
+
+--S 722 of 994
+--d0:=D(m0,x)
+--E 722
+
+)clear all
+
+--S 723 of 994
+t0:=1/(sqrt(1-x^2)*sqrt(2+3*x^2))
+--R
+--R
+--R 1
+--R (1) ---------------------
+--R +--------+ +-------+
+--R | 2 | 2
+--R \|- x + 1 \|3x + 2
+--R Type: Expression(Integer)
+--E 723
+
+--S 724 of 994
+--r0:=elliptic_f(asin(x),-3/2)/sqrt(2)
+--E 724
+
+--S 725 of 994
+--a0:=integrate(t0,x)
+--E 725
+
+--S 726 of 994
+--m0:=a0-r0
+--E 726
+
+--S 727 of 994
+--d0:=D(m0,x)
+--E 727
+
+)clear all
+
+--S 728 of 994
+t0:=1/(sqrt(2-3*x^2)*sqrt(1-x^2))
+--R
+--R
+--R 1
+--R (1) -----------------------
+--R +---------+ +--------+
+--R | 2 | 2
+--R \|- 3x + 2 \|- x + 1
+--R Type: Expression(Integer)
+--E 728
+
+--S 729 of 994
+--r0:=elliptic_f(asin(x),3/2)/sqrt(2)
+--E 729
+
+--S 730 of 994
+--a0:=integrate(t0,x)
+--E 730
+
+--S 731 of 994
+--m0:=a0-r0
+--E 731
+
+--S 732 of 994
+--d0:=D(m0,x)
+--E 732
+
+)clear all
+
+--S 733 of 994
+t0:=1/(sqrt(4-x^2)*sqrt(2+3*x^2))
+--R
+--R
+--R 1
+--R (1) ---------------------
+--R +--------+ +-------+
+--R | 2 | 2
+--R \|- x + 4 \|3x + 2
+--R Type: Expression(Integer)
+--E 733
+
+--S 734 of 994
+--r0:=elliptic_f(asin(1/2*x),-6)/sqrt(2)
+--E 734
+
+--S 735 of 994
+--a0:=integrate(t0,x)
+--E 735
+
+--S 736 of 994
+--m0:=a0-r0
+--E 736
+
+--S 737 of 994
+--d0:=D(m0,x)
+--E 737
+
+)clear all
+
+--S 738 of 994
+t0:=1/(sqrt(2-3*x^2)*sqrt(4-x^2))
+--R
+--R
+--R 1
+--R (1) -----------------------
+--R +---------+ +--------+
+--R | 2 | 2
+--R \|- 3x + 2 \|- x + 4
+--R Type: Expression(Integer)
+--E 738
+
+--S 739 of 994
+--r0:=elliptic_f(asin(1/2*x),6)/sqrt(2)
+--E 739
+
+--S 740 of 994
+--a0:=integrate(t0,x)
+--E 740
+
+--S 741 of 994
+--m0:=a0-r0
+--E 741
+
+--S 742 of 994
+--d0:=D(m0,x)
+--E 742
+
+)clear all
+
+--S 743 of 994
+t0:=1/(sqrt(1-4*x^2)*sqrt(2+3*x^2))
+--R
+--R
+--R 1
+--R (1) ----------------------
+--R +---------+ +-------+
+--R | 2 | 2
+--R \|- 4x + 1 \|3x + 2
+--R Type: Expression(Integer)
+--E 743
+
+--S 744 of 994
+--r0:=1/2*elliptic_f(asin(2*x),-3/8)/sqrt(2)
+--E 744
+
+--S 745 of 994
+--a0:=integrate(t0,x)
+--E 745
+
+--S 746 of 994
+--m0:=a0-r0
+--E 746
+
+--S 747 of 994
+--d0:=D(m0,x)
+--E 747
+
+)clear all
+
+--S 748 of 994
+t0:=1/(sqrt(1-4*x^2)*sqrt(2-3*x^2))
+--R
+--R
+--R 1
+--R (1) ------------------------
+--R +---------+ +---------+
+--R | 2 | 2
+--R \|- 4x + 1 \|- 3x + 2
+--R Type: Expression(Integer)
+--E 748
+
+--S 749 of 994
+--r0:=1/2*elliptic_f(asin(2*x),3/8)/sqrt(2)
+--E 749
+
+--S 750 of 994
+--a0:=integrate(t0,x)
+--E 750
+
+--S 751 of 994
+--m0:=a0-r0
+--E 751
+
+--S 752 of 994
+--d0:=D(m0,x)
+--E 752
+
+)clear all
+
+--S 753 of 994
+t0:=1/(sqrt(1+x^2)*sqrt(2+3*x^2))
+--R
+--R
+--R 1
+--R (1) -------------------
+--R +------+ +-------+
+--R | 2 | 2
+--R \|x + 1 \|3x + 2
+--R Type: Expression(Integer)
+--E 753
+
+--S 754 of 994
+--r0:=-%i*elliptic_f(%i*asinh(x),3/2)/sqrt(2)
+--E 754
+
+--S 755 of 994
+--a0:=integrate(t0,x)
+--E 755
+
+--S 756 of 994
+--m0:=a0-r0
+--E 756
+
+--S 757 of 994
+--d0:=D(m0,x)
+--E 757
+
+)clear all
+
+--S 758 of 994
+t0:=1/(sqrt(2-3*x^2)*sqrt(1+x^2))
+--R
+--R
+--R 1
+--R (1) ---------------------
+--R +---------+ +------+
+--R | 2 | 2
+--R \|- 3x + 2 \|x + 1
+--R Type: Expression(Integer)
+--E 758
+
+--S 759 of 994
+--r0:=elliptic_f(asin(x*sqrt(3/2)),-2/3)/sqrt(3)
+--E 759
+
+--S 760 of 994
+--a0:=integrate(t0,x)
+--E 760
+
+--S 761 of 994
+--m0:=a0-r0
+--E 761
+
+--S 762 of 994
+--d0:=D(m0,x)
+--E 762
+
+)clear all
+
+--S 763 of 994
+t0:=1/(sqrt(4+x^2)*sqrt(2+3*x^2))
+--R
+--R
+--R 1
+--R (1) -------------------
+--R +------+ +-------+
+--R | 2 | 2
+--R \|x + 4 \|3x + 2
+--R Type: Expression(Integer)
+--E 763
+
+--S 764 of 994
+--r0:=-%i*elliptic_f(%i*asinh(1/2*x),6)/sqrt(2)
+--E 764
+
+--S 765 of 994
+--a0:=integrate(t0,x)
+--E 765
+
+--S 766 of 994
+--m0:=a0-r0
+--E 766
+
+--S 767 of 994
+--d0:=D(m0,x)
+--E 767
+
+)clear all
+
+--S 768 of 994
+t0:=1/(sqrt(2-3*x^2)*sqrt(4+x^2))
+--R
+--R
+--R 1
+--R (1) ---------------------
+--R +---------+ +------+
+--R | 2 | 2
+--R \|- 3x + 2 \|x + 4
+--R Type: Expression(Integer)
+--E 768
+
+--S 769 of 994
+--r0:=1/2*elliptic_f(asin(x*sqrt(3/2)),-1/6)/sqrt(3)
+--E 769
+
+--S 770 of 994
+--a0:=integrate(t0,x)
+--E 770
+
+--S 771 of 994
+--m0:=a0-r0
+--E 771
+
+--S 772 of 994
+--d0:=D(m0,x)
+--E 772
+
+)clear all
+
+--S 773 of 994
+t0:=1/(sqrt(2+3*x^2)*sqrt(1+4*x^2))
+--R
+--R
+--R 1
+--R (1) --------------------
+--R +-------+ +-------+
+--R | 2 | 2
+--R \|3x + 2 \|4x + 1
+--R Type: Expression(Integer)
+--E 773
+
+--S 774 of 994
+--r0:=-1/2*%i*elliptic_f(%i*asinh(2*x),3/8)/sqrt(2)
+--E 774
+
+--S 775 of 994
+--a0:=integrate(t0,x)
+--E 775
+
+--S 776 of 994
+--m0:=a0-r0
+--E 776
+
+--S 777 of 994
+--d0:=D(m0,x)
+--E 777
+
+)clear all
+
+--S 778 of 994
+t0:=1/(sqrt(2-3*x^2)*sqrt(1+4*x^2))
+--R
+--R
+--R 1
+--R (1) ----------------------
+--R +---------+ +-------+
+--R | 2 | 2
+--R \|- 3x + 2 \|4x + 1
+--R Type: Expression(Integer)
+--E 778
+
+--S 779 of 994
+--r0:=elliptic_f(asin(x*sqrt(3/2)),-8/3)/sqrt(3)
+--E 779
+
+--S 780 of 994
+--a0:=integrate(t0,x)
+--E 780
+
+--S 781 of 994
+--m0:=a0-r0
+--E 781
+
+--S 782 of 994
+--d0:=D(m0,x)
+--E 782
+
+)clear all
+
+--S 783 of 994
+t0:=1/(sqrt(1-x^2)*sqrt(-1+2*x^2))
+--R
+--R
+--R 1
+--R (1) ---------------------
+--R +--------+ +-------+
+--R | 2 | 2
+--R \|- x + 1 \|2x - 1
+--R Type: Expression(Integer)
+--E 783
+
+--S 784 of 994
+--r0:=-elliptic_f(acos(x),2),elliptic_f(asin(x),2)*sqrt(1-2*x^2)/sqrt(-1+2*x^2)
+--E 784
+
+--S 785 of 994
+--a0:=integrate(t0,x)
+--E 785
+
+--S 786 of 994
+--m0:=a0-r0
+--E 786
+
+--S 787 of 994
+--d0:=D(m0,x)
+--E 787
+
+)clear all
+
+--S 788 of 994
+t0:=sqrt(2+b*x^2)/sqrt(3+d*x^2)
+--R
+--R
+--R +--------+
+--R | 2
+--R \|b x + 2
+--R (1) -----------
+--R +--------+
+--R | 2
+--R \|d x + 3
+--R Type: Expression(Integer)
+--E 788
+
+--S 789 of 994
+--r0:=elliptic_e(asin(x*sqrt(-d)/sqrt(3)),3/2*b/d)*sqrt(2)/sqrt(-d)
+--E 789
+
+--S 790 of 994
+--a0:=integrate(t0,x)
+--E 790
+
+--S 791 of 994
+--m0:=a0-r0
+--E 791
+
+--S 792 of 994
+--d0:=D(m0,x)
+--E 792
+
+)clear all
+
+--S 793 of 994
+t0:=sqrt(a+b*x^2)/sqrt(c+d*x^2)
+--R
+--R
+--R +--------+
+--R | 2
+--R \|b x + a
+--R (1) -----------
+--R +--------+
+--R | 2
+--R \|d x + c
+--R Type: Expression(Integer)
+--E 793
+
+--S 794 of 994
+--r0:=elliptic_e(asin(x*sqrt(-d)/sqrt(c)),b*c/(a*d))*sqrt(c)*_
+-- sqrt(a+b*x^2)*sqrt((c+d*x^2)/c)/(sqrt(-d)*sqrt((a+b*x^2)/a)*_
+-- sqrt(c+d*x^2))
+--E 794
+
+--S 795 of 994
+--a0:=integrate(t0,x)
+--E 795
+
+--S 796 of 994
+--m0:=a0-r0
+--E 796
+
+--S 797 of 994
+--d0:=D(m0,x)
+--E 797
+
+)clear all
+
+--S 798 of 994
+t0:=sqrt(-1+3*x^2)/sqrt(2-3*x^2)
+--R
+--R
+--R +-------+
+--R | 2
+--R \|3x - 1
+--R (1) ------------
+--R +---------+
+--R | 2
+--R \|- 3x + 2
+--R Type: Expression(Integer)
+--E 798
+
+--S 799 of 994
+--r0:=elliptic_e(asin(x*sqrt(3/2)),2)*sqrt(-1+3*x^2)/(sqrt(3)*sqrt(1-3*x^2))
+--E 799
+
+--S 800 of 994
+--a0:=integrate(t0,x)
+--E 800
+
+--S 801 of 994
+--m0:=a0-r0
+--E 801
+
+--S 802 of 994
+--d0:=D(m0,x)
+--E 802
+
+)clear all
+
+--S 803 of 994
+t0:=sqrt(1+2*c*x^2/(b-sqrt(b^2-4*a*c)))/sqrt(1+2*c*x^2/(b+sqrt(b^2-4*a*c)))
+--R
+--R
+--R +--------------------------+
+--R | +-----------+
+--R | | 2 2
+--R |\|- 4a c + b - 2c x - b
+--R |--------------------------
+--R | +-----------+
+--R | | 2
+--R \| \|- 4a c + b - b
+--R (1) -----------------------------
+--R +--------------------------+
+--R | +-----------+
+--R | | 2 2
+--R |\|- 4a c + b + 2c x + b
+--R |--------------------------
+--R | +-----------+
+--R | | 2
+--R \| \|- 4a c + b + b
+--R Type: Expression(Integer)
+--E 803
+
+--S 804 of 994
+--r0:=elliptic_e(asin(x*sqrt(2)*sqrt(-c)/sqrt(b+sqrt(b^2-4*a*c))),_
+-- (b+sqrt(b^2-4*a*c))/(b-sqrt(b^2-4*a*c)))*sqrt(b+_
+-- sqrt(b^2-4*a*c))/(sqrt(2)*sqrt(-c))
+--E 804
+
+--S 805 of 994
+--a0:=integrate(t0,x)
+--E 805
+
+--S 806 of 994
+--m0:=a0-r0
+--E 806
+
+--S 807 of 994
+--d0:=D(m0,x)
+--E 807
+
+)clear all
+
+--S 808 of 994
+t0:=(a+b*x^3)*(c+d*x^3)^p
+--R
+--R
+--R 3 3 p
+--R (1) (b x + a)(d x + c)
+--R Type: Expression(Integer)
+--E 808
+
+--S 809 of 994
+--r0:=b*x*(c+d*x^3)^(1+p)/(d*(4+3*p))-(b*c-a*d*(4+3*p))*x*(c+d*x^3)^p*_
+-- hypergeometric(1/3,-p,4/3,-d*x^3/c)/(d*(4+3*p)*((c+d*x^3)/c)^p)
+--E 809
+
+--S 810 of 994
+--a0:=integrate(t0,x)
+--E 810
+
+--S 811 of 994
+--m0:=a0-r0
+--E 811
+
+--S 812 of 994
+--d0:=D(m0,x)
+--E 812
+
+)clear all
+
+--S 813 of 994
+t0:=(a+b*x^3)*(c+d*x^3)^4
+--R
+--R
+--R (1)
+--R 4 15 4 3 12 3 2 2 9
+--R b d x + (a d + 4b c d )x + (4a c d + 6b c d )x
+--R +
+--R 2 2 3 6 3 4 3 4
+--R (6a c d + 4b c d)x + (4a c d + b c )x + a c
+--R Type: Polynomial(Integer)
+--E 813
+
+--S 814 of 994
+r0:=a*c^4*x+1/4*c^3*(b*c+4*a*d)*x^4+2/7*c^2*d*(2*b*c+3*a*d)*x^7+_
+ 1/5*c*d^2*(3*b*c+2*a*d)*x^10+1/13*d^3*(4*b*c+a*d)*x^13+1/16*b*d^4*x^16
+--R
+--R
+--R (2)
+--R 1 4 16 1 4 4 3 13 2 3 3 2 2 10
+--R -- b d x + (-- a d + -- b c d )x + (- a c d + - b c d )x
+--R 16 13 13 5 5
+--R +
+--R 6 2 2 4 3 7 3 1 4 4 4
+--R (- a c d + - b c d)x + (a c d + - b c )x + a c x
+--R 7 7 4
+--R Type: Polynomial(Fraction(Integer))
+--E 814
+
+--S 815 of 994
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 1 4 16 1 4 4 3 13 2 3 3 2 2 10
+--R -- b d x + (-- a d + -- b c d )x + (- a c d + - b c d )x
+--R 16 13 13 5 5
+--R +
+--R 6 2 2 4 3 7 3 1 4 4 4
+--R (- a c d + - b c d)x + (a c d + - b c )x + a c x
+--R 7 7 4
+--R Type: Polynomial(Fraction(Integer))
+--E 815
+
+--S 816 of 994
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Polynomial(Fraction(Integer))
+--E 816
+
+--S 817 of 994
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Polynomial(Fraction(Integer))
+--E 817
+
+)clear all
+
+--S 818 of 994
+t0:=(a+b*x^3)*(c+d*x^3)^3
+--R
+--R
+--R (1)
+--R 3 12 3 2 9 2 2 6 2 3 3
+--R b d x + (a d + 3b c d )x + (3a c d + 3b c d)x + (3a c d + b c )x
+--R +
+--R 3
+--R a c
+--R Type: Polynomial(Integer)
+--E 818
+
+--S 819 of 994
+r0:=a*c^3*x+1/4*c^2*(b*c+3*a*d)*x^4+3/7*c*d*(b*c+a*d)*x^7+_
+ 1/10*d^2*(3*b*c+a*d)*x^10+1/13*b*d^3*x^13
+--R
+--R
+--R (2)
+--R 1 3 13 1 3 3 2 10 3 2 3 2 7
+--R -- b d x + (-- a d + -- b c d )x + (- a c d + - b c d)x
+--R 13 10 10 7 7
+--R +
+--R 3 2 1 3 4 3
+--R (- a c d + - b c )x + a c x
+--R 4 4
+--R Type: Polynomial(Fraction(Integer))
+--E 819
+
+--S 820 of 994
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 1 3 13 1 3 3 2 10 3 2 3 2 7
+--R -- b d x + (-- a d + -- b c d )x + (- a c d + - b c d)x
+--R 13 10 10 7 7
+--R +
+--R 3 2 1 3 4 3
+--R (- a c d + - b c )x + a c x
+--R 4 4
+--R Type: Polynomial(Fraction(Integer))
+--E 820
+
+--S 821 of 994
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Polynomial(Fraction(Integer))
+--E 821
+
+--S 822 of 994
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Polynomial(Fraction(Integer))
+--E 822
+
+)clear all
+
+--S 823 of 994
+t0:=(a+b*x^3)*(c+d*x^3)^2
+--R
+--R
+--R 2 9 2 6 2 3 2
+--R (1) b d x + (a d + 2b c d)x + (2a c d + b c )x + a c
+--R Type: Polynomial(Integer)
+--E 823
+
+--S 824 of 994
+r0:=a*c^2*x+1/4*c*(b*c+2*a*d)*x^4+1/7*d*(2*b*c+a*d)*x^7+1/10*b*d^2*x^10
+--R
+--R
+--R 1 2 10 1 2 2 7 1 1 2 4 2
+--R (2) -- b d x + (- a d + - b c d)x + (- a c d + - b c )x + a c x
+--R 10 7 7 2 4
+--R Type: Polynomial(Fraction(Integer))
+--E 824
+
+--S 825 of 994
+a0:=integrate(t0,x)
+--R
+--R
+--R 1 2 10 1 2 2 7 1 1 2 4 2
+--R (3) -- b d x + (- a d + - b c d)x + (- a c d + - b c )x + a c x
+--R 10 7 7 2 4
+--R Type: Polynomial(Fraction(Integer))
+--E 825
+
+--S 826 of 994
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Polynomial(Fraction(Integer))
+--E 826
+
+--S 827 of 994
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Polynomial(Fraction(Integer))
+--E 827
+
+)clear all
+
+--S 828 of 994
+t0:=(a+b*x^3)*(c+d*x^3)
+--R
+--R
+--R 6 3
+--R (1) b d x + (a d + b c)x + a c
+--R Type: Polynomial(Integer)
+--E 828
+
+--S 829 of 994
+r0:=a*c*x+1/4*(b*c+a*d)*x^4+1/7*b*d*x^7
+--R
+--R
+--R 1 7 1 1 4
+--R (2) - b d x + (- a d + - b c)x + a c x
+--R 7 4 4
+--R Type: Polynomial(Fraction(Integer))
+--E 829
+
+--S 830 of 994
+a0:=integrate(t0,x)
+--R
+--R
+--R 1 7 1 1 4
+--R (3) - b d x + (- a d + - b c)x + a c x
+--R 7 4 4
+--R Type: Polynomial(Fraction(Integer))
+--E 830
+
+--S 831 of 994
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Polynomial(Fraction(Integer))
+--E 831
+
+--S 832 of 994
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Polynomial(Fraction(Integer))
+--E 832
+
+)clear all
+
+--S 833 of 994
+t0:=(a+b*x^3)/(c+d*x^3)
+--R
+--R
+--R 3
+--R b x + a
+--R (1) --------
+--R 3
+--R d x + c
+--R Type: Fraction(Polynomial(Integer))
+--E 833
+
+--S 834 of 994
+r0:=b*x/d-1/3*(b*c-a*d)*log(c^(1/3)+d^(1/3)*x)/(c^(2/3)*d^(4/3))+_
+ 1/6*(b*c-a*d)*log(c^(2/3)-c^(1/3)*d^(1/3)*x+d^(2/3)*x^2)/_
+ (c^(2/3)*d^(4/3))+(b*c-a*d)*atan((c^(1/3)-2*d^(1/3)*x)/_
+ (c^(1/3)*sqrt(3)))/(c^(2/3)*d^(4/3)*sqrt(3))
+--R
+--R
+--R (2)
+--R +-+ 2 3+-+2 3+-+3+-+ 3+-+2
+--R (- a d + b c)\|3 log(x \|d - x\|c \|d + \|c )
+--R +
+--R 3+-+ 3+-+
+--R +-+ 3+-+ 3+-+ 2x\|d - \|c
+--R (2a d - 2b c)\|3 log(x\|d + \|c ) + (6a d - 6b c)atan(-------------)
+--R +-+3+-+
+--R \|3 \|c
+--R +
+--R +-+3+-+2 3+-+
+--R 6b x\|3 \|c \|d
+--R /
+--R +-+3+-+2 3+-+
+--R 6d\|3 \|c \|d
+--R Type: Expression(Integer)
+--E 834
+
+--S 835 of 994
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +---+2 +---+
+--R +-+ 2 3| 2 3| 2 2
+--R (- a d + b c)\|3 log(x \|c d - c x\|c d + c )
+--R +
+--R +---+
+--R +-+ 3| 2
+--R (2a d - 2b c)\|3 log(x\|c d + c)
+--R +
+--R +---+
+--R +-+3| 2 +-+ +---+
+--R 2x\|3 \|c d - c\|3 +-+3| 2
+--R (6a d - 6b c)atan(--------------------) + 6b x\|3 \|c d
+--R 3c
+--R /
+--R +---+
+--R +-+3| 2
+--R 6d\|3 \|c d
+--R Type: Union(Expression(Integer),...)
+--E 835
+
+--S 836 of 994
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +---+2 +---+
+--R +-+3+-+2 3+-+ 2 3| 2 3| 2 2
+--R (- a d + b c)\|3 \|c \|d log(x \|c d - c x\|c d + c )
+--R +
+--R +---+
+--R +-+3+-+2 3+-+ 3| 2
+--R (2a d - 2b c)\|3 \|c \|d log(x\|c d + c)
+--R +
+--R +---+
+--R +-+3| 2 2 3+-+2 3+-+3+-+ 3+-+2
+--R (a d - b c)\|3 \|c d log(x \|d - x\|c \|d + \|c )
+--R +
+--R +---+
+--R +-+3| 2 3+-+ 3+-+
+--R (- 2a d + 2b c)\|3 \|c d log(x\|d + \|c )
+--R +
+--R +---+
+--R +-+3| 2 +-+
+--R 3+-+2 3+-+ 2x\|3 \|c d - c\|3
+--R (6a d - 6b c)\|c \|d atan(--------------------)
+--R 3c
+--R +
+--R +---+ 3+-+ 3+-+
+--R 3| 2 2x\|d - \|c
+--R (- 6a d + 6b c)\|c d atan(-------------)
+--R +-+3+-+
+--R \|3 \|c
+--R /
+--R +---+
+--R +-+3+-+2 3+-+3| 2
+--R 6d\|3 \|c \|d \|c d
+--R Type: Expression(Integer)
+--E 836
+
+--S 837 of 994
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 837
+
+)clear all
+
+--S 838 of 994
+t0:=(a+b*x^3)/(c+d*x^3)^2
+--R
+--R
+--R 3
+--R b x + a
+--R (1) -------------------
+--R 2 6 3 2
+--R d x + 2c d x + c
+--R Type: Fraction(Polynomial(Integer))
+--E 838
+
+--S 839 of 994
+r0:=-1/3*(b*c-a*d)*x/(c*d*(c+d*x^3))+1/9*(b*c+2*a*d)*log(c^(1/3)+_
+ d^(1/3)*x)/(c^(5/3)*d^(4/3))-1/18*(b*c+2*a*d)*log(c^(2/3)-_
+ c^(1/3)*d^(1/3)*x+d^(2/3)*x^2)/(c^(5/3)*d^(4/3))-1/3*(b*c+_
+ 2*a*d)*atan((c^(1/3)-2*d^(1/3)*x)/(c^(1/3)*sqrt(3)))/_
+ (c^(5/3)*d^(4/3)*sqrt(3))
+--R
+--R
+--R (2)
+--R 2 3 2 +-+ 2 3+-+2 3+-+3+-+ 3+-+2
+--R ((- 2a d - b c d)x - 2a c d - b c )\|3 log(x \|d - x\|c \|d + \|c )
+--R +
+--R 2 3 2 +-+ 3+-+ 3+-+
+--R ((4a d + 2b c d)x + 4a c d + 2b c )\|3 log(x\|d + \|c )
+--R +
+--R 3+-+ 3+-+
+--R 2 3 2 2x\|d - \|c
+--R ((12a d + 6b c d)x + 12a c d + 6b c )atan(-------------)
+--R +-+3+-+
+--R \|3 \|c
+--R +
+--R +-+3+-+2 3+-+
+--R (6a d - 6b c)x\|3 \|c \|d
+--R /
+--R 2 3 2 +-+3+-+2 3+-+
+--R (18c d x + 18c d)\|3 \|c \|d
+--R Type: Expression(Integer)
+--E 839
+
+--S 840 of 994
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +---+2 +---+
+--R 2 3 2 +-+ 2 3| 2 3| 2 2
+--R ((- 2a d - b c d)x - 2a c d - b c )\|3 log(x \|c d - c x\|c d + c )
+--R +
+--R +---+
+--R 2 3 2 +-+ 3| 2
+--R ((4a d + 2b c d)x + 4a c d + 2b c )\|3 log(x\|c d + c)
+--R +
+--R +---+
+--R +-+3| 2 +-+
+--R 2 3 2 2x\|3 \|c d - c\|3
+--R ((12a d + 6b c d)x + 12a c d + 6b c )atan(--------------------)
+--R 3c
+--R +
+--R +---+
+--R +-+3| 2
+--R (6a d - 6b c)x\|3 \|c d
+--R /
+--R +---+
+--R 2 3 2 +-+3| 2
+--R (18c d x + 18c d)\|3 \|c d
+--R Type: Union(Expression(Integer),...)
+--E 840
+
+--S 841 of 994
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +---+2 +---+
+--R +-+3+-+2 3+-+ 2 3| 2 3| 2 2
+--R (- 2a d - b c)\|3 \|c \|d log(x \|c d - c x\|c d + c )
+--R +
+--R +---+
+--R +-+3+-+2 3+-+ 3| 2
+--R (4a d + 2b c)\|3 \|c \|d log(x\|c d + c)
+--R +
+--R +---+
+--R +-+3| 2 2 3+-+2 3+-+3+-+ 3+-+2
+--R (2a d + b c)\|3 \|c d log(x \|d - x\|c \|d + \|c )
+--R +
+--R +---+
+--R +-+3| 2 3+-+ 3+-+
+--R (- 4a d - 2b c)\|3 \|c d log(x\|d + \|c )
+--R +
+--R +---+
+--R +-+3| 2 +-+
+--R 3+-+2 3+-+ 2x\|3 \|c d - c\|3
+--R (12a d + 6b c)\|c \|d atan(--------------------)
+--R 3c
+--R +
+--R +---+ 3+-+ 3+-+
+--R 3| 2 2x\|d - \|c
+--R (- 12a d - 6b c)\|c d atan(-------------)
+--R +-+3+-+
+--R \|3 \|c
+--R /
+--R +---+
+--R +-+3+-+2 3+-+3| 2
+--R 18c d\|3 \|c \|d \|c d
+--R Type: Expression(Integer)
+--E 841
+
+--S 842 of 994
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 842
+
+)clear all
+
+--S 843 of 994
+t0:=(a+b*x^3)/(c+d*x^3)^3
+--R
+--R
+--R 3
+--R b x + a
+--R (1) -----------------------------
+--R 3 9 2 6 2 3 3
+--R d x + 3c d x + 3c d x + c
+--R Type: Fraction(Polynomial(Integer))
+--E 843
+
+--S 844 of 994
+r0:=-1/6*(b*c-a*d)*x/(c*d*(c+d*x^3)^2)+1/18*(b*c+5*a*d)*x/_
+ (c^2*d*(c+d*x^3))+1/27*(b*c+5*a*d)*log(c^(1/3)+d^(1/3)*x)/_
+ (c^(8/3)*d^(4/3))-1/54*(b*c+5*a*d)*log(c^(2/3)-c^(1/3)*d^(1/3)*_
+ x+d^(2/3)*x^2)/(c^(8/3)*d^(4/3))-1/9*(b*c+5*a*d)*_
+ atan((c^(1/3)-2*d^(1/3)*x)/(c^(1/3)*sqrt(3)))/(c^(8/3)*d^(4/3)*sqrt(3))
+--R
+--R
+--R (2)
+--R 3 2 6 2 2 3 2 3 +-+
+--R ((- 5a d - b c d )x + (- 10a c d - 2b c d)x - 5a c d - b c )\|3
+--R *
+--R 2 3+-+2 3+-+3+-+ 3+-+2
+--R log(x \|d - x\|c \|d + \|c )
+--R +
+--R 3 2 6 2 2 3 2 3 +-+
+--R ((10a d + 2b c d )x + (20a c d + 4b c d)x + 10a c d + 2b c )\|3
+--R *
+--R 3+-+ 3+-+
+--R log(x\|d + \|c )
+--R +
+--R 3 2 6 2 2 3 2 3
+--R ((30a d + 6b c d )x + (60a c d + 12b c d)x + 30a c d + 6b c )
+--R *
+--R 3+-+ 3+-+
+--R 2x\|d - \|c
+--R atan(-------------)
+--R +-+3+-+
+--R \|3 \|c
+--R +
+--R 2 4 2 +-+3+-+2 3+-+
+--R ((15a d + 3b c d)x + (24a c d - 6b c )x)\|3 \|c \|d
+--R /
+--R 2 3 6 3 2 3 4 +-+3+-+2 3+-+
+--R (54c d x + 108c d x + 54c d)\|3 \|c \|d
+--R Type: Expression(Integer)
+--E 844
+
+--S 845 of 994
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 3 2 6 2 2 3 2 3 +-+
+--R ((- 5a d - b c d )x + (- 10a c d - 2b c d)x - 5a c d - b c )\|3
+--R *
+--R +---+2 +---+
+--R 2 3| 2 3| 2 2
+--R log(x \|c d - c x\|c d + c )
+--R +
+--R 3 2 6 2 2 3 2 3 +-+
+--R ((10a d + 2b c d )x + (20a c d + 4b c d)x + 10a c d + 2b c )\|3
+--R *
+--R +---+
+--R 3| 2
+--R log(x\|c d + c)
+--R +
+--R 3 2 6 2 2 3 2 3
+--R ((30a d + 6b c d )x + (60a c d + 12b c d)x + 30a c d + 6b c )
+--R *
+--R +---+
+--R +-+3| 2 +-+
+--R 2x\|3 \|c d - c\|3
+--R atan(--------------------)
+--R 3c
+--R +
+--R +---+
+--R 2 4 2 +-+3| 2
+--R ((15a d + 3b c d)x + (24a c d - 6b c )x)\|3 \|c d
+--R /
+--R +---+
+--R 2 3 6 3 2 3 4 +-+3| 2
+--R (54c d x + 108c d x + 54c d)\|3 \|c d
+--R Type: Union(Expression(Integer),...)
+--E 845
+
+--S 846 of 994
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +---+2 +---+
+--R +-+3+-+2 3+-+ 2 3| 2 3| 2 2
+--R (- 5a d - b c)\|3 \|c \|d log(x \|c d - c x\|c d + c )
+--R +
+--R +---+
+--R +-+3+-+2 3+-+ 3| 2
+--R (10a d + 2b c)\|3 \|c \|d log(x\|c d + c)
+--R +
+--R +---+
+--R +-+3| 2 2 3+-+2 3+-+3+-+ 3+-+2
+--R (5a d + b c)\|3 \|c d log(x \|d - x\|c \|d + \|c )
+--R +
+--R +---+
+--R +-+3| 2 3+-+ 3+-+
+--R (- 10a d - 2b c)\|3 \|c d log(x\|d + \|c )
+--R +
+--R +---+
+--R +-+3| 2 +-+
+--R 3+-+2 3+-+ 2x\|3 \|c d - c\|3
+--R (30a d + 6b c)\|c \|d atan(--------------------)
+--R 3c
+--R +
+--R +---+ 3+-+ 3+-+
+--R 3| 2 2x\|d - \|c
+--R (- 30a d - 6b c)\|c d atan(-------------)
+--R +-+3+-+
+--R \|3 \|c
+--R /
+--R +---+
+--R 2 +-+3+-+2 3+-+3| 2
+--R 54c d\|3 \|c \|d \|c d
+--R Type: Expression(Integer)
+--E 846
+
+--S 847 of 994
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 847
+
+)clear all
+
+--S 848 of 994
+t0:=(a+b*x^3)^2*(c+d*x^3)^p
+--R
+--R
+--R 2 6 3 2 3 p
+--R (1) (b x + 2a b x + a )(d x + c)
+--R Type: Expression(Integer)
+--E 848
+
+--S 849 of 994
+--r0:=-b*(4*b*c-a*d*(10+3*p))*x*(c+d*x^3)^(1+p)/(d^2*(4+3*p)*(7+3*p))+_
+-- b*x*(a+b*x^3)*(c+d*x^3)^(1+p)/(d*(7+3*p))+(4*b^2*c^2-2*a*b*c*_
+-- d*(7+3*p)+a^2*d^2*(28+33*p+9*p^2))*x*(c+d*x^3)^p*_
+-- hypergeometric(1/3,-p,4/3,-d*x^3/c)/(d^2*(4+3*p)*(7+3*p)*((c+d*x^3)/c)^p)
+--E 849
+
+--S 850 of 994
+--a0:=integrate(t0,x)
+--E 850
+
+--S 851 of 994
+--m0:=a0-r0
+--E 851
+
+--S 852 of 994
+--d0:=D(m0,x)
+--E 852
+
+)clear all
+
+--S 853 of 994
+t0:=(a+b*x^3)^2*(c+d*x^3)^3
+--R
+--R
+--R (1)
+--R 2 3 15 3 2 2 12 2 3 2 2 2 9
+--R b d x + (2a b d + 3b c d )x + (a d + 6a b c d + 3b c d)x
+--R +
+--R 2 2 2 2 3 6 2 2 3 3 2 3
+--R (3a c d + 6a b c d + b c )x + (3a c d + 2a b c )x + a c
+--R Type: Polynomial(Integer)
+--E 853
+
+--S 854 of 994
+r0:=a^2*c^3*x+1/4*a*c^2*(2*b*c+3*a*d)*x^4+1/7*c*(b^2*c^2+6*a*b*c*d+_
+ 3*a^2*d^2)*x^7+1/10*d*(3*b^2*c^2+6*a*b*c*d+a^2*d^2)*x^10+_
+ 1/13*b*d^2*(3*b*c+2*a*d)*x^13+1/16*b^2*d^3*x^16
+--R
+--R
+--R (2)
+--R 1 2 3 16 2 3 3 2 2 13
+--R -- b d x + (-- a b d + -- b c d )x
+--R 16 13 13
+--R +
+--R 1 2 3 3 2 3 2 2 10 3 2 2 6 2 1 2 3 7
+--R (-- a d + - a b c d + -- b c d)x + (- a c d + - a b c d + - b c )x
+--R 10 5 10 7 7 7
+--R +
+--R 3 2 2 1 3 4 2 3
+--R (- a c d + - a b c )x + a c x
+--R 4 2
+--R Type: Polynomial(Fraction(Integer))
+--E 854
+
+--S 855 of 994
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 1 2 3 16 2 3 3 2 2 13
+--R -- b d x + (-- a b d + -- b c d )x
+--R 16 13 13
+--R +
+--R 1 2 3 3 2 3 2 2 10 3 2 2 6 2 1 2 3 7
+--R (-- a d + - a b c d + -- b c d)x + (- a c d + - a b c d + - b c )x
+--R 10 5 10 7 7 7
+--R +
+--R 3 2 2 1 3 4 2 3
+--R (- a c d + - a b c )x + a c x
+--R 4 2
+--R Type: Polynomial(Fraction(Integer))
+--E 855
+
+--S 856 of 994
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Polynomial(Fraction(Integer))
+--E 856
+
+--S 857 of 994
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Polynomial(Fraction(Integer))
+--E 857
+
+)clear all
+
+--S 858 of 994
+t0:=(a+b*x^3)^2*(c+d*x^3)^2
+--R
+--R
+--R (1)
+--R 2 2 12 2 2 9 2 2 2 2 6
+--R b d x + (2a b d + 2b c d)x + (a d + 4a b c d + b c )x
+--R +
+--R 2 2 3 2 2
+--R (2a c d + 2a b c )x + a c
+--R Type: Polynomial(Integer)
+--E 858
+
+--S 859 of 994
+r0:=a^2*c^2*x+1/2*a*c*(b*c+a*d)*x^4+1/7*(b^2*c^2+4*a*b*c*d+a^2*d^2)*x^7+_
+ 1/5*b*d*(b*c+a*d)*x^10+1/13*b^2*d^2*x^13
+--R
+--R
+--R (2)
+--R 1 2 2 13 1 2 1 2 10 1 2 2 4 1 2 2 7
+--R -- b d x + (- a b d + - b c d)x + (- a d + - a b c d + - b c )x
+--R 13 5 5 7 7 7
+--R +
+--R 1 2 1 2 4 2 2
+--R (- a c d + - a b c )x + a c x
+--R 2 2
+--R Type: Polynomial(Fraction(Integer))
+--E 859
+
+--S 860 of 994
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 1 2 2 13 1 2 1 2 10 1 2 2 4 1 2 2 7
+--R -- b d x + (- a b d + - b c d)x + (- a d + - a b c d + - b c )x
+--R 13 5 5 7 7 7
+--R +
+--R 1 2 1 2 4 2 2
+--R (- a c d + - a b c )x + a c x
+--R 2 2
+--R Type: Polynomial(Fraction(Integer))
+--E 860
+
+--S 861 of 994
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Polynomial(Fraction(Integer))
+--E 861
+
+--S 862 of 994
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Polynomial(Fraction(Integer))
+--E 862
+
+)clear all
+
+--S 863 of 994
+t0:=(a+b*x^3)^2*(c+d*x^3)
+--R
+--R
+--R 2 9 2 6 2 3 2
+--R (1) b d x + (2a b d + b c)x + (a d + 2a b c)x + a c
+--R Type: Polynomial(Integer)
+--E 863
+
+--S 864 of 994
+r0:=a^2*c*x+1/4*a*(2*b*c+a*d)*x^4+1/7*b*(b*c+2*a*d)*x^7+1/10*b^2*d*x^10
+--R
+--R
+--R 1 2 10 2 1 2 7 1 2 1 4 2
+--R (2) -- b d x + (- a b d + - b c)x + (- a d + - a b c)x + a c x
+--R 10 7 7 4 2
+--R Type: Polynomial(Fraction(Integer))
+--E 864
+
+--S 865 of 994
+a0:=integrate(t0,x)
+--R
+--R
+--R 1 2 10 2 1 2 7 1 2 1 4 2
+--R (3) -- b d x + (- a b d + - b c)x + (- a d + - a b c)x + a c x
+--R 10 7 7 4 2
+--R Type: Polynomial(Fraction(Integer))
+--E 865
+
+--S 866 of 994
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Polynomial(Fraction(Integer))
+--E 866
+
+--S 867 of 994
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Polynomial(Fraction(Integer))
+--E 867
+
+)clear all
+
+--S 868 of 994
+t0:=(a+b*x^3)^2/(c+d*x^3)
+--R
+--R
+--R 2 6 3 2
+--R b x + 2a b x + a
+--R (1) -------------------
+--R 3
+--R d x + c
+--R Type: Fraction(Polynomial(Integer))
+--E 868
+
+--S 869 of 994
+r0:=-b*(b*c-2*a*d)*x/d^2+1/4*b^2*x^4/d+1/3*(b*c-a*d)^2*log(c^(1/3)+_
+ d^(1/3)*x)/(c^(2/3)*d^(7/3))-1/6*(b*c-a*d)^2*log(c^(2/3)-_
+ c^(1/3)*d^(1/3)*x+d^(2/3)*x^2)/(c^(2/3)*d^(7/3))-(b*c-a*d)^2*_
+ atan((c^(1/3)-2*d^(1/3)*x)/(c^(1/3)*sqrt(3)))/(c^(2/3)*d^(7/3)*sqrt(3))
+--R
+--R
+--R (2)
+--R 2 2 2 2 +-+ 2 3+-+2 3+-+3+-+ 3+-+2
+--R (- 2a d + 4a b c d - 2b c )\|3 log(x \|d - x\|c \|d + \|c )
+--R +
+--R 2 2 2 2 +-+ 3+-+ 3+-+
+--R (4a d - 8a b c d + 4b c )\|3 log(x\|d + \|c )
+--R +
+--R 3+-+ 3+-+
+--R 2 2 2 2 2x\|d - \|c
+--R (12a d - 24a b c d + 12b c )atan(-------------)
+--R +-+3+-+
+--R \|3 \|c
+--R +
+--R 2 4 2 +-+3+-+2 3+-+
+--R (3b d x + (24a b d - 12b c)x)\|3 \|c \|d
+--R /
+--R 2 +-+3+-+2 3+-+
+--R 12d \|3 \|c \|d
+--R Type: Expression(Integer)
+--E 869
+
+--S 870 of 994
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +---+2 +---+
+--R 2 2 2 2 +-+ 2 3| 2 3| 2 2
+--R (- 2a d + 4a b c d - 2b c )\|3 log(x \|c d - c x\|c d + c )
+--R +
+--R +---+
+--R 2 2 2 2 +-+ 3| 2
+--R (4a d - 8a b c d + 4b c )\|3 log(x\|c d + c)
+--R +
+--R +---+
+--R +-+3| 2 +-+
+--R 2 2 2 2 2x\|3 \|c d - c\|3
+--R (12a d - 24a b c d + 12b c )atan(--------------------)
+--R 3c
+--R +
+--R +---+
+--R 2 4 2 +-+3| 2
+--R (3b d x + (24a b d - 12b c)x)\|3 \|c d
+--R /
+--R +---+
+--R 2 +-+3| 2
+--R 12d \|3 \|c d
+--R Type: Union(Expression(Integer),...)
+--E 870
+
+--S 871 of 994
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +---+2 +---+
+--R 2 2 2 2 +-+3+-+2 3+-+ 2 3| 2 3| 2 2
+--R (- a d + 2a b c d - b c )\|3 \|c \|d log(x \|c d - c x\|c d + c )
+--R +
+--R +---+
+--R 2 2 2 2 +-+3+-+2 3+-+ 3| 2
+--R (2a d - 4a b c d + 2b c )\|3 \|c \|d log(x\|c d + c)
+--R +
+--R +---+
+--R 2 2 2 2 +-+3| 2 2 3+-+2 3+-+3+-+ 3+-+2
+--R (a d - 2a b c d + b c )\|3 \|c d log(x \|d - x\|c \|d + \|c )
+--R +
+--R +---+
+--R 2 2 2 2 +-+3| 2 3+-+ 3+-+
+--R (- 2a d + 4a b c d - 2b c )\|3 \|c d log(x\|d + \|c )
+--R +
+--R +---+
+--R +-+3| 2 +-+
+--R 2 2 2 2 3+-+2 3+-+ 2x\|3 \|c d - c\|3
+--R (6a d - 12a b c d + 6b c )\|c \|d atan(--------------------)
+--R 3c
+--R +
+--R +---+ 3+-+ 3+-+
+--R 2 2 2 2 3| 2 2x\|d - \|c
+--R (- 6a d + 12a b c d - 6b c )\|c d atan(-------------)
+--R +-+3+-+
+--R \|3 \|c
+--R /
+--R +---+
+--R 2 +-+3+-+2 3+-+3| 2
+--R 6d \|3 \|c \|d \|c d
+--R Type: Expression(Integer)
+--E 871
+
+--S 872 of 994
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 872
+
+)clear all
+
+--S 873 of 994
+t0:=(a+b*x^3)^2/(c+d*x^3)^2
+--R
+--R
+--R 2 6 3 2
+--R b x + 2a b x + a
+--R (1) -------------------
+--R 2 6 3 2
+--R d x + 2c d x + c
+--R Type: Fraction(Polynomial(Integer))
+--E 873
+
+--S 874 of 994
+r0:=b^2*x/d^2+1/3*(b*c-a*d)^2*x/(c*d^2*(c+d*x^3))-2/9*(b*c-a*d)*_
+ (2*b*c+a*d)*log(c^(1/3)+d^(1/3)*x)/(c^(5/3)*d^(7/3))+1/9*_
+ (b*c-a*d)*(2*b*c+a*d)*log(c^(2/3)-c^(1/3)*d^(1/3)*x+d^(2/3)*_
+ x^2)/(c^(5/3)*d^(7/3))+2/3*(b*c-a*d)*(2*b*c+a*d)*_
+ atan((c^(1/3)-2*d^(1/3)*x)/(c^(1/3)*sqrt(3)))/(c^(5/3)*d^(7/3)*sqrt(3))
+--R
+--R
+--R (2)
+--R 2 3 2 2 2 3 2 2 2 2 3 +-+
+--R ((- a d - a b c d + 2b c d)x - a c d - a b c d + 2b c )\|3
+--R *
+--R 2 3+-+2 3+-+3+-+ 3+-+2
+--R log(x \|d - x\|c \|d + \|c )
+--R +
+--R 2 3 2 2 2 3 2 2 2 2 3 +-+
+--R ((2a d + 2a b c d - 4b c d)x + 2a c d + 2a b c d - 4b c )\|3
+--R *
+--R 3+-+ 3+-+
+--R log(x\|d + \|c )
+--R +
+--R 2 3 2 2 2 3 2 2 2 2 3
+--R ((6a d + 6a b c d - 12b c d)x + 6a c d + 6a b c d - 12b c )
+--R *
+--R 3+-+ 3+-+
+--R 2x\|d - \|c
+--R atan(-------------)
+--R +-+3+-+
+--R \|3 \|c
+--R +
+--R 2 4 2 2 2 2 +-+3+-+2 3+-+
+--R (9b c d x + (3a d - 6a b c d + 12b c )x)\|3 \|c \|d
+--R /
+--R 3 3 2 2 +-+3+-+2 3+-+
+--R (9c d x + 9c d )\|3 \|c \|d
+--R Type: Expression(Integer)
+--E 874
+
+--S 875 of 994
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 2 3 2 2 2 3 2 2 2 2 3 +-+
+--R ((- a d - a b c d + 2b c d)x - a c d - a b c d + 2b c )\|3
+--R *
+--R +---+2 +---+
+--R 2 3| 2 3| 2 2
+--R log(x \|c d - c x\|c d + c )
+--R +
+--R 2 3 2 2 2 3 2 2 2 2 3 +-+
+--R ((2a d + 2a b c d - 4b c d)x + 2a c d + 2a b c d - 4b c )\|3
+--R *
+--R +---+
+--R 3| 2
+--R log(x\|c d + c)
+--R +
+--R 2 3 2 2 2 3 2 2 2 2 3
+--R ((6a d + 6a b c d - 12b c d)x + 6a c d + 6a b c d - 12b c )
+--R *
+--R +---+
+--R +-+3| 2 +-+
+--R 2x\|3 \|c d - c\|3
+--R atan(--------------------)
+--R 3c
+--R +
+--R +---+
+--R 2 4 2 2 2 2 +-+3| 2
+--R (9b c d x + (3a d - 6a b c d + 12b c )x)\|3 \|c d
+--R /
+--R +---+
+--R 3 3 2 2 +-+3| 2
+--R (9c d x + 9c d )\|3 \|c d
+--R Type: Union(Expression(Integer),...)
+--E 875
+
+--S 876 of 994
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +---+2 +---+
+--R 2 2 2 2 +-+3+-+2 3+-+ 2 3| 2 3| 2 2
+--R (- a d - a b c d + 2b c )\|3 \|c \|d log(x \|c d - c x\|c d + c )
+--R +
+--R +---+
+--R 2 2 2 2 +-+3+-+2 3+-+ 3| 2
+--R (2a d + 2a b c d - 4b c )\|3 \|c \|d log(x\|c d + c)
+--R +
+--R +---+
+--R 2 2 2 2 +-+3| 2 2 3+-+2 3+-+3+-+ 3+-+2
+--R (a d + a b c d - 2b c )\|3 \|c d log(x \|d - x\|c \|d + \|c )
+--R +
+--R +---+
+--R 2 2 2 2 +-+3| 2 3+-+ 3+-+
+--R (- 2a d - 2a b c d + 4b c )\|3 \|c d log(x\|d + \|c )
+--R +
+--R +---+
+--R +-+3| 2 +-+
+--R 2 2 2 2 3+-+2 3+-+ 2x\|3 \|c d - c\|3
+--R (6a d + 6a b c d - 12b c )\|c \|d atan(--------------------)
+--R 3c
+--R +
+--R +---+ 3+-+ 3+-+
+--R 2 2 2 2 3| 2 2x\|d - \|c
+--R (- 6a d - 6a b c d + 12b c )\|c d atan(-------------)
+--R +-+3+-+
+--R \|3 \|c
+--R /
+--R +---+
+--R 2 +-+3+-+2 3+-+3| 2
+--R 9c d \|3 \|c \|d \|c d
+--R Type: Expression(Integer)
+--E 876
+
+--S 877 of 994
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 877
+
+)clear all
+
+--S 878 of 994
+t0:=(a+b*x^3)^2/(c+d*x^3)^3
+--R
+--R
+--R 2 6 3 2
+--R b x + 2a b x + a
+--R (1) -----------------------------
+--R 3 9 2 6 2 3 3
+--R d x + 3c d x + 3c d x + c
+--R Type: Fraction(Polynomial(Integer))
+--E 878
+
+--S 879 of 994
+r0:=-1/6*(b*c-a*d)*x*(a+b*x^3)/(c*d*(c+d*x^3)^2)-1/18*(b*c-a*d)*_
+ (4*b*c+5*a*d)*x/(c^2*d^2*(c+d*x^3))+1/27*(2*b^2*c^2+2*a*b*c*_
+ d+5*a^2*d^2)*log(c^(1/3)+d^(1/3)*x)/(c^(8/3)*d^(7/3))-1/54*_
+ (2*b^2*c^2+2*a*b*c*d+5*a^2*d^2)*log(c^(2/3)-c^(1/3)*d^(1/3)*_
+ x+d^(2/3)*x^2)/(c^(8/3)*d^(7/3))-1/9*(2*b^2*c^2+2*a*b*c*d+_
+ 5*a^2*d^2)*atan((c^(1/3)-2*d^(1/3)*x)/(c^(1/3)*sqrt(3)))/_
+ (c^(8/3)*d^(7/3)*sqrt(3))
+--R
+--R
+--R (2)
+--R 2 4 3 2 2 2 6
+--R (- 5a d - 2a b c d - 2b c d )x
+--R +
+--R 2 3 2 2 2 3 3 2 2 2 3 2 4
+--R (- 10a c d - 4a b c d - 4b c d)x - 5a c d - 2a b c d - 2b c
+--R *
+--R +-+ 2 3+-+2 3+-+3+-+ 3+-+2
+--R \|3 log(x \|d - x\|c \|d + \|c )
+--R +
+--R 2 4 3 2 2 2 6 2 3 2 2 2 3 3
+--R (10a d + 4a b c d + 4b c d )x + (20a c d + 8a b c d + 8b c d)x
+--R +
+--R 2 2 2 3 2 4
+--R 10a c d + 4a b c d + 4b c
+--R *
+--R +-+ 3+-+ 3+-+
+--R \|3 log(x\|d + \|c )
+--R +
+--R 2 4 3 2 2 2 6
+--R (30a d + 12a b c d + 12b c d )x
+--R +
+--R 2 3 2 2 2 3 3 2 2 2 3 2 4
+--R (60a c d + 24a b c d + 24b c d)x + 30a c d + 12a b c d + 12b c
+--R *
+--R 3+-+ 3+-+
+--R 2x\|d - \|c
+--R atan(-------------)
+--R +-+3+-+
+--R \|3 \|c
+--R +
+--R 2 3 2 2 2 4 2 2 2 2 3
+--R ((15a d + 6a b c d - 21b c d)x + (24a c d - 12a b c d - 12b c )x)
+--R *
+--R +-+3+-+2 3+-+
+--R \|3 \|c \|d
+--R /
+--R 2 4 6 3 3 3 4 2 +-+3+-+2 3+-+
+--R (54c d x + 108c d x + 54c d )\|3 \|c \|d
+--R Type: Expression(Integer)
+--E 879
+
+--S 880 of 994
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 2 4 3 2 2 2 6
+--R (- 5a d - 2a b c d - 2b c d )x
+--R +
+--R 2 3 2 2 2 3 3 2 2 2 3 2 4
+--R (- 10a c d - 4a b c d - 4b c d)x - 5a c d - 2a b c d - 2b c
+--R *
+--R +---+2 +---+
+--R +-+ 2 3| 2 3| 2 2
+--R \|3 log(x \|c d - c x\|c d + c )
+--R +
+--R 2 4 3 2 2 2 6 2 3 2 2 2 3 3
+--R (10a d + 4a b c d + 4b c d )x + (20a c d + 8a b c d + 8b c d)x
+--R +
+--R 2 2 2 3 2 4
+--R 10a c d + 4a b c d + 4b c
+--R *
+--R +---+
+--R +-+ 3| 2
+--R \|3 log(x\|c d + c)
+--R +
+--R 2 4 3 2 2 2 6
+--R (30a d + 12a b c d + 12b c d )x
+--R +
+--R 2 3 2 2 2 3 3 2 2 2 3 2 4
+--R (60a c d + 24a b c d + 24b c d)x + 30a c d + 12a b c d + 12b c
+--R *
+--R +---+
+--R +-+3| 2 +-+
+--R 2x\|3 \|c d - c\|3
+--R atan(--------------------)
+--R 3c
+--R +
+--R 2 3 2 2 2 4 2 2 2 2 3
+--R ((15a d + 6a b c d - 21b c d)x + (24a c d - 12a b c d - 12b c )x)
+--R *
+--R +---+
+--R +-+3| 2
+--R \|3 \|c d
+--R /
+--R +---+
+--R 2 4 6 3 3 3 4 2 +-+3| 2
+--R (54c d x + 108c d x + 54c d )\|3 \|c d
+--R Type: Union(Expression(Integer),...)
+--E 880
+
+--S 881 of 994
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +---+2 +---+
+--R 2 2 2 2 +-+3+-+2 3+-+ 2 3| 2 3| 2 2
+--R (- 5a d - 2a b c d - 2b c )\|3 \|c \|d log(x \|c d - c x\|c d + c )
+--R +
+--R +---+
+--R 2 2 2 2 +-+3+-+2 3+-+ 3| 2
+--R (10a d + 4a b c d + 4b c )\|3 \|c \|d log(x\|c d + c)
+--R +
+--R +---+
+--R 2 2 2 2 +-+3| 2 2 3+-+2 3+-+3+-+ 3+-+2
+--R (5a d + 2a b c d + 2b c )\|3 \|c d log(x \|d - x\|c \|d + \|c )
+--R +
+--R +---+
+--R 2 2 2 2 +-+3| 2 3+-+ 3+-+
+--R (- 10a d - 4a b c d - 4b c )\|3 \|c d log(x\|d + \|c )
+--R +
+--R +---+
+--R +-+3| 2 +-+
+--R 2 2 2 2 3+-+2 3+-+ 2x\|3 \|c d - c\|3
+--R (30a d + 12a b c d + 12b c )\|c \|d atan(--------------------)
+--R 3c
+--R +
+--R +---+ 3+-+ 3+-+
+--R 2 2 2 2 3| 2 2x\|d - \|c
+--R (- 30a d - 12a b c d - 12b c )\|c d atan(-------------)
+--R +-+3+-+
+--R \|3 \|c
+--R /
+--R +---+
+--R 2 2 +-+3+-+2 3+-+3| 2
+--R 54c d \|3 \|c \|d \|c d
+--R Type: Expression(Integer)
+--E 881
+
+--S 882 of 994
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 882
+
+)clear all
+
+--S 883 of 994
+t0:=(c+d*x^3)^p/(a+b*x^3)
+--R
+--R
+--R 3 p
+--R (d x + c)
+--R (1) -----------
+--R 3
+--R b x + a
+--R Type: Expression(Integer)
+--E 883
+
+--S 884 of 994
+--r0:=x*(c+d*x^3)^p*AppellF1(1/3,1,-p,4/3,-b*x^3/a,-d*x^3/c)/(a*(1+d*x^3/c)^p)
+--E 884
+
+--S 885 of 994
+--a0:=integrate(t0,x)
+--E 885
+
+--S 886 of 994
+--m0:=a0-r0
+--E 886
+
+--S 887 of 994
+--d0:=D(m0,x)
+--E 887
+
+)clear all
+
+--S 888 of 994
+t0:=(c+d*x^3)^4/(a+b*x^3)
+--R
+--R
+--R 4 12 3 9 2 2 6 3 3 4
+--R d x + 4c d x + 6c d x + 4c d x + c
+--R (1) ----------------------------------------
+--R 3
+--R b x + a
+--R Type: Fraction(Polynomial(Integer))
+--E 888
+
+--S 889 of 994
+r0:=d*(2*b*c-a*d)*(2*b^2*c^2-2*a*b*c*d+a^2*d^2)*x/b^4+1/4*d^2*_
+ (6*b^2*c^2-4*a*b*c*d+a^2*d^2)*x^4/b^3+1/7*d^3*(4*b*c-a*d)*_
+ x^7/b^2+1/10*d^4*x^10/b+1/3*(b*c-a*d)^4*log(a^(1/3)+b^(1/3)*_
+ x)/(a^(2/3)*b^(13/3))-1/6*(b*c-a*d)^4*log(a^(2/3)-a^(1/3)*_
+ b^(1/3)*x+b^(2/3)*x^2)/(a^(2/3)*b^(13/3))-(b*c-a*d)^4*_
+ atan((a^(1/3)-2*b^(1/3)*x)/(a^(1/3)*sqrt(3)))/(a^(2/3)*b^(13/3)*sqrt(3))
+--R
+--R
+--R (2)
+--R 4 4 3 3 2 2 2 2 3 3 4 4 +-+
+--R (- 70a d + 280a b c d - 420a b c d + 280a b c d - 70b c )\|3
+--R *
+--R 2 3+-+2 3+-+3+-+ 3+-+2
+--R log(x \|b - x\|a \|b + \|a )
+--R +
+--R 4 4 3 3 2 2 2 2 3 3 4 4 +-+
+--R (140a d - 560a b c d + 840a b c d - 560a b c d + 140b c )\|3
+--R *
+--R 3+-+ 3+-+
+--R log(x\|b + \|a )
+--R +
+--R 4 4 3 3 2 2 2 2 3 3 4 4
+--R (420a d - 1680a b c d + 2520a b c d - 1680a b c d + 420b c )
+--R *
+--R 3+-+ 3+-+
+--R 2x\|b - \|a
+--R atan(-------------)
+--R +-+3+-+
+--R \|3 \|a
+--R +
+--R 3 4 10 2 4 3 3 7
+--R 42b d x + (- 60a b d + 240b c d )x
+--R +
+--R 2 4 2 3 3 2 2 4
+--R (105a b d - 420a b c d + 630b c d )x
+--R +
+--R 3 4 2 3 2 2 2 3 3
+--R (- 420a d + 1680a b c d - 2520a b c d + 1680b c d)x
+--R *
+--R +-+3+-+2 3+-+
+--R \|3 \|a \|b
+--R /
+--R 4 +-+3+-+2 3+-+
+--R 420b \|3 \|a \|b
+--R Type: Expression(Integer)
+--E 889
+
+--S 890 of 994
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 4 4 3 3 2 2 2 2 3 3 4 4 +-+
+--R (- 70a d + 280a b c d - 420a b c d + 280a b c d - 70b c )\|3
+--R *
+--R +---+2 +---+
+--R 2 3| 2 3| 2 2
+--R log(x \|a b - a x\|a b + a )
+--R +
+--R 4 4 3 3 2 2 2 2 3 3 4 4 +-+
+--R (140a d - 560a b c d + 840a b c d - 560a b c d + 140b c )\|3
+--R *
+--R +---+
+--R 3| 2
+--R log(x\|a b + a)
+--R +
+--R 4 4 3 3 2 2 2 2 3 3 4 4
+--R (420a d - 1680a b c d + 2520a b c d - 1680a b c d + 420b c )
+--R *
+--R +---+
+--R +-+3| 2 +-+
+--R 2x\|3 \|a b - a\|3
+--R atan(--------------------)
+--R 3a
+--R +
+--R 3 4 10 2 4 3 3 7
+--R 42b d x + (- 60a b d + 240b c d )x
+--R +
+--R 2 4 2 3 3 2 2 4
+--R (105a b d - 420a b c d + 630b c d )x
+--R +
+--R 3 4 2 3 2 2 2 3 3
+--R (- 420a d + 1680a b c d - 2520a b c d + 1680b c d)x
+--R *
+--R +---+
+--R +-+3| 2
+--R \|3 \|a b
+--R /
+--R +---+
+--R 4 +-+3| 2
+--R 420b \|3 \|a b
+--R Type: Union(Expression(Integer),...)
+--E 890
+
+--S 891 of 994
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R 4 4 3 3 2 2 2 2 3 3 4 4 +-+3+-+2 3+-+
+--R (- a d + 4a b c d - 6a b c d + 4a b c d - b c )\|3 \|a \|b
+--R *
+--R +---+2 +---+
+--R 2 3| 2 3| 2 2
+--R log(x \|a b - a x\|a b + a )
+--R +
+--R 4 4 3 3 2 2 2 2 3 3 4 4 +-+3+-+2 3+-+
+--R (2a d - 8a b c d + 12a b c d - 8a b c d + 2b c )\|3 \|a \|b
+--R *
+--R +---+
+--R 3| 2
+--R log(x\|a b + a)
+--R +
+--R +---+
+--R 4 4 3 3 2 2 2 2 3 3 4 4 +-+3| 2
+--R (a d - 4a b c d + 6a b c d - 4a b c d + b c )\|3 \|a b
+--R *
+--R 2 3+-+2 3+-+3+-+ 3+-+2
+--R log(x \|b - x\|a \|b + \|a )
+--R +
+--R +---+
+--R 4 4 3 3 2 2 2 2 3 3 4 4 +-+3| 2
+--R (- 2a d + 8a b c d - 12a b c d + 8a b c d - 2b c )\|3 \|a b
+--R *
+--R 3+-+ 3+-+
+--R log(x\|b + \|a )
+--R +
+--R 4 4 3 3 2 2 2 2 3 3 4 4 3+-+2 3+-+
+--R (6a d - 24a b c d + 36a b c d - 24a b c d + 6b c )\|a \|b
+--R *
+--R +---+
+--R +-+3| 2 +-+
+--R 2x\|3 \|a b - a\|3
+--R atan(--------------------)
+--R 3a
+--R +
+--R +---+
+--R 4 4 3 3 2 2 2 2 3 3 4 4 3| 2
+--R (- 6a d + 24a b c d - 36a b c d + 24a b c d - 6b c )\|a b
+--R *
+--R 3+-+ 3+-+
+--R 2x\|b - \|a
+--R atan(-------------)
+--R +-+3+-+
+--R \|3 \|a
+--R /
+--R +---+
+--R 4 +-+3+-+2 3+-+3| 2
+--R 6b \|3 \|a \|b \|a b
+--R Type: Expression(Integer)
+--E 891
+
+--S 892 of 994
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 892
+
+)clear all
+
+--S 893 of 994
+t0:=(c+d*x^3)^3/(a+b*x^3)
+--R
+--R
+--R 3 9 2 6 2 3 3
+--R d x + 3c d x + 3c d x + c
+--R (1) -----------------------------
+--R 3
+--R b x + a
+--R Type: Fraction(Polynomial(Integer))
+--E 893
+
+--S 894 of 994
+r0:=d*(3*b^2*c^2-3*a*b*c*d+a^2*d^2)*x/b^3+1/4*d^2*(3*b*c-a*d)*x^4/b^2+_
+ 1/7*d^3*x^7/b+1/3*(b*c-a*d)^3*log(a^(1/3)+b^(1/3)*x)/(a^(2/3)*_
+ b^(10/3))-1/6*(b*c-a*d)^3*log(a^(2/3)-a^(1/3)*b^(1/3)*x+b^(2/3)*_
+ x^2)/(a^(2/3)*b^(10/3))-(b*c-a*d)^3*atan((a^(1/3)-2*b^(1/3)*x)/_
+ (a^(1/3)*sqrt(3)))/(a^(2/3)*b^(10/3)*sqrt(3))
+--R
+--R
+--R (2)
+--R 3 3 2 2 2 2 3 3 +-+
+--R (14a d - 42a b c d + 42a b c d - 14b c )\|3
+--R *
+--R 2 3+-+2 3+-+3+-+ 3+-+2
+--R log(x \|b - x\|a \|b + \|a )
+--R +
+--R 3 3 2 2 2 2 3 3 +-+ 3+-+ 3+-+
+--R (- 28a d + 84a b c d - 84a b c d + 28b c )\|3 log(x\|b + \|a )
+--R +
+--R 3+-+ 3+-+
+--R 3 3 2 2 2 2 3 3 2x\|b - \|a
+--R (- 84a d + 252a b c d - 252a b c d + 84b c )atan(-------------)
+--R +-+3+-+
+--R \|3 \|a
+--R +
+--R 2 3 7 3 2 2 4
+--R 12b d x + (- 21a b d + 63b c d )x
+--R +
+--R 2 3 2 2 2
+--R (84a d - 252a b c d + 252b c d)x
+--R *
+--R +-+3+-+2 3+-+
+--R \|3 \|a \|b
+--R /
+--R 3 +-+3+-+2 3+-+
+--R 84b \|3 \|a \|b
+--R Type: Expression(Integer)
+--E 894
+
+--S 895 of 994
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 3 3 2 2 2 2 3 3 +-+
+--R (- 14a d + 42a b c d - 42a b c d + 14b c )\|3
+--R *
+--R +-----+2 +-----+
+--R 2 3| 2 3| 2 2
+--R log(x \|- a b + a x\|- a b + a )
+--R +
+--R +-----+
+--R 3 3 2 2 2 2 3 3 +-+ 3| 2
+--R (28a d - 84a b c d + 84a b c d - 28b c )\|3 log(x\|- a b - a)
+--R +
+--R 3 3 2 2 2 2 3 3
+--R (- 84a d + 252a b c d - 252a b c d + 84b c )
+--R *
+--R +-----+
+--R +-+3| 2 +-+
+--R 2x\|3 \|- a b + a\|3
+--R atan(----------------------)
+--R 3a
+--R +
+--R 2 3 7 3 2 2 4
+--R 12b d x + (- 21a b d + 63b c d )x
+--R +
+--R 2 3 2 2 2
+--R (84a d - 252a b c d + 252b c d)x
+--R *
+--R +-----+
+--R +-+3| 2
+--R \|3 \|- a b
+--R /
+--R +-----+
+--R 3 +-+3| 2
+--R 84b \|3 \|- a b
+--R Type: Union(Expression(Integer),...)
+--E 895
+
+--S 896 of 994
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +-----+
+--R 3 3 2 2 2 2 3 3 +-+3| 2
+--R (- a d + 3a b c d - 3a b c d + b c )\|3 \|- a b
+--R *
+--R 2 3+-+2 3+-+3+-+ 3+-+2
+--R log(x \|b - x\|a \|b + \|a )
+--R +
+--R +-----+
+--R 3 3 2 2 2 2 3 3 +-+3| 2 3+-+ 3+-+
+--R (2a d - 6a b c d + 6a b c d - 2b c )\|3 \|- a b log(x\|b + \|a )
+--R +
+--R 3 3 2 2 2 2 3 3 +-+3+-+2 3+-+
+--R (- a d + 3a b c d - 3a b c d + b c )\|3 \|a \|b
+--R *
+--R +-----+2 +-----+
+--R 2 3| 2 3| 2 2
+--R log(x \|- a b + a x\|- a b + a )
+--R +
+--R +-----+
+--R 3 3 2 2 2 2 3 3 +-+3+-+2 3+-+ 3| 2
+--R (2a d - 6a b c d + 6a b c d - 2b c )\|3 \|a \|b log(x\|- a b - a)
+--R +
+--R +-----+ 3+-+ 3+-+
+--R 3 3 2 2 2 2 3 3 3| 2 2x\|b - \|a
+--R (6a d - 18a b c d + 18a b c d - 6b c )\|- a b atan(-------------)
+--R +-+3+-+
+--R \|3 \|a
+--R +
+--R 3 3 2 2 2 2 3 3 3+-+2 3+-+
+--R (- 6a d + 18a b c d - 18a b c d + 6b c )\|a \|b
+--R *
+--R +-----+
+--R +-+3| 2 +-+
+--R 2x\|3 \|- a b + a\|3
+--R atan(----------------------)
+--R 3a
+--R /
+--R +-----+
+--R 3 +-+3| 2 3+-+2 3+-+
+--R 6b \|3 \|- a b \|a \|b
+--R Type: Expression(Integer)
+--E 896
+
+--S 897 of 994
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 897
+
+)clear all
+
+--S 898 of 994
+t0:=(c+d*x^3)^2/(a+b*x^3)
+--R
+--R
+--R 2 6 3 2
+--R d x + 2c d x + c
+--R (1) -------------------
+--R 3
+--R b x + a
+--R Type: Fraction(Polynomial(Integer))
+--E 898
+
+--S 899 of 994
+r0:=d*(2*b*c-a*d)*x/b^2+1/4*d^2*x^4/b+1/3*(b*c-a*d)^2*log(a^(1/3)+_
+ b^(1/3)*x)/(a^(2/3)*b^(7/3))-1/6*(b*c-a*d)^2*log(a^(2/3)-_
+ a^(1/3)*b^(1/3)*x+b^(2/3)*x^2)/(a^(2/3)*b^(7/3))-(b*c-a*d)^2*_
+ atan((a^(1/3)-2*b^(1/3)*x)/(a^(1/3)*sqrt(3)))/(a^(2/3)*b^(7/3)*sqrt(3))
+--R
+--R
+--R (2)
+--R 2 2 2 2 +-+ 2 3+-+2 3+-+3+-+ 3+-+2
+--R (- 2a d + 4a b c d - 2b c )\|3 log(x \|b - x\|a \|b + \|a )
+--R +
+--R 2 2 2 2 +-+ 3+-+ 3+-+
+--R (4a d - 8a b c d + 4b c )\|3 log(x\|b + \|a )
+--R +
+--R 3+-+ 3+-+
+--R 2 2 2 2 2x\|b - \|a
+--R (12a d - 24a b c d + 12b c )atan(-------------)
+--R +-+3+-+
+--R \|3 \|a
+--R +
+--R 2 4 2 +-+3+-+2 3+-+
+--R (3b d x + (- 12a d + 24b c d)x)\|3 \|a \|b
+--R /
+--R 2 +-+3+-+2 3+-+
+--R 12b \|3 \|a \|b
+--R Type: Expression(Integer)
+--E 899
+
+--S 900 of 994
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +---+2 +---+
+--R 2 2 2 2 +-+ 2 3| 2 3| 2 2
+--R (- 2a d + 4a b c d - 2b c )\|3 log(x \|a b - a x\|a b + a )
+--R +
+--R +---+
+--R 2 2 2 2 +-+ 3| 2
+--R (4a d - 8a b c d + 4b c )\|3 log(x\|a b + a)
+--R +
+--R +---+
+--R +-+3| 2 +-+
+--R 2 2 2 2 2x\|3 \|a b - a\|3
+--R (12a d - 24a b c d + 12b c )atan(--------------------)
+--R 3a
+--R +
+--R +---+
+--R 2 4 2 +-+3| 2
+--R (3b d x + (- 12a d + 24b c d)x)\|3 \|a b
+--R /
+--R +---+
+--R 2 +-+3| 2
+--R 12b \|3 \|a b
+--R Type: Union(Expression(Integer),...)
+--E 900
+
+--S 901 of 994
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +---+2 +---+
+--R 2 2 2 2 +-+3+-+2 3+-+ 2 3| 2 3| 2 2
+--R (- a d + 2a b c d - b c )\|3 \|a \|b log(x \|a b - a x\|a b + a )
+--R +
+--R +---+
+--R 2 2 2 2 +-+3+-+2 3+-+ 3| 2
+--R (2a d - 4a b c d + 2b c )\|3 \|a \|b log(x\|a b + a)
+--R +
+--R +---+
+--R 2 2 2 2 +-+3| 2 2 3+-+2 3+-+3+-+ 3+-+2
+--R (a d - 2a b c d + b c )\|3 \|a b log(x \|b - x\|a \|b + \|a )
+--R +
+--R +---+
+--R 2 2 2 2 +-+3| 2 3+-+ 3+-+
+--R (- 2a d + 4a b c d - 2b c )\|3 \|a b log(x\|b + \|a )
+--R +
+--R +---+
+--R +-+3| 2 +-+
+--R 2 2 2 2 3+-+2 3+-+ 2x\|3 \|a b - a\|3
+--R (6a d - 12a b c d + 6b c )\|a \|b atan(--------------------)
+--R 3a
+--R +
+--R +---+ 3+-+ 3+-+
+--R 2 2 2 2 3| 2 2x\|b - \|a
+--R (- 6a d + 12a b c d - 6b c )\|a b atan(-------------)
+--R +-+3+-+
+--R \|3 \|a
+--R /
+--R +---+
+--R 2 +-+3+-+2 3+-+3| 2
+--R 6b \|3 \|a \|b \|a b
+--R Type: Expression(Integer)
+--E 901
+
+--S 902 of 994
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 902
+
+)clear all
+
+--S 903 of 994
+t0:=(c+d*x^3)/(a+b*x^3)
+--R
+--R
+--R 3
+--R d x + c
+--R (1) --------
+--R 3
+--R b x + a
+--R Type: Fraction(Polynomial(Integer))
+--E 903
+
+--S 904 of 994
+r0:=d*x/b+1/3*(b*c-a*d)*log(a^(1/3)+b^(1/3)*x)/(a^(2/3)*b^(4/3))-_
+ 1/6*(b*c-a*d)*log(a^(2/3)-a^(1/3)*b^(1/3)*x+b^(2/3)*x^2)/_
+ (a^(2/3)*b^(4/3))-(b*c-a*d)*atan((a^(1/3)-2*b^(1/3)*x)/_
+ (a^(1/3)*sqrt(3)))/(a^(2/3)*b^(4/3)*sqrt(3))
+--R
+--R
+--R (2)
+--R +-+ 2 3+-+2 3+-+3+-+ 3+-+2
+--R (a d - b c)\|3 log(x \|b - x\|a \|b + \|a )
+--R +
+--R 3+-+ 3+-+
+--R +-+ 3+-+ 3+-+ 2x\|b - \|a
+--R (- 2a d + 2b c)\|3 log(x\|b + \|a ) + (- 6a d + 6b c)atan(-------------)
+--R +-+3+-+
+--R \|3 \|a
+--R +
+--R +-+3+-+2 3+-+
+--R 6d x\|3 \|a \|b
+--R /
+--R +-+3+-+2 3+-+
+--R 6b\|3 \|a \|b
+--R Type: Expression(Integer)
+--E 904
+
+--S 905 of 994
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +-----+2 +-----+
+--R +-+ 2 3| 2 3| 2 2
+--R (- a d + b c)\|3 log(x \|- a b + a x\|- a b + a )
+--R +
+--R +-----+
+--R +-+ 3| 2
+--R (2a d - 2b c)\|3 log(x\|- a b - a)
+--R +
+--R +-----+
+--R +-+3| 2 +-+ +-----+
+--R 2x\|3 \|- a b + a\|3 +-+3| 2
+--R (- 6a d + 6b c)atan(----------------------) + 6d x\|3 \|- a b
+--R 3a
+--R /
+--R +-----+
+--R +-+3| 2
+--R 6b\|3 \|- a b
+--R Type: Union(Expression(Integer),...)
+--E 905
+
+--S 906 of 994
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +-----+
+--R +-+3| 2 2 3+-+2 3+-+3+-+ 3+-+2
+--R (- a d + b c)\|3 \|- a b log(x \|b - x\|a \|b + \|a )
+--R +
+--R +-----+
+--R +-+3| 2 3+-+ 3+-+
+--R (2a d - 2b c)\|3 \|- a b log(x\|b + \|a )
+--R +
+--R +-----+2 +-----+
+--R +-+3+-+2 3+-+ 2 3| 2 3| 2 2
+--R (- a d + b c)\|3 \|a \|b log(x \|- a b + a x\|- a b + a )
+--R +
+--R +-----+
+--R +-+3+-+2 3+-+ 3| 2
+--R (2a d - 2b c)\|3 \|a \|b log(x\|- a b - a)
+--R +
+--R +-----+ 3+-+ 3+-+
+--R 3| 2 2x\|b - \|a
+--R (6a d - 6b c)\|- a b atan(-------------)
+--R +-+3+-+
+--R \|3 \|a
+--R +
+--R +-----+
+--R +-+3| 2 +-+
+--R 3+-+2 3+-+ 2x\|3 \|- a b + a\|3
+--R (- 6a d + 6b c)\|a \|b atan(----------------------)
+--R 3a
+--R /
+--R +-----+
+--R +-+3| 2 3+-+2 3+-+
+--R 6b\|3 \|- a b \|a \|b
+--R Type: Expression(Integer)
+--E 906
+
+--S 907 of 994
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 907
+
+)clear all
+
+--S 908 of 994
+t0:=1/((a+b*x^3)*(c+d*x^3))
+--R
+--R
+--R 1
+--R (1) ----------------------------
+--R 6 3
+--R b d x + (a d + b c)x + a c
+--R Type: Fraction(Polynomial(Integer))
+--E 908
+
+--S 909 of 994
+r0:=1/3*b^(2/3)*log(a^(1/3)+b^(1/3)*x)/(a^(2/3)*(b*c-a*d))-_
+ 1/3*d^(2/3)*log(c^(1/3)+d^(1/3)*x)/(c^(2/3)*(b*c-a*d))-_
+ 1/6*b^(2/3)*log(a^(2/3)-a^(1/3)*b^(1/3)*x+b^(2/3)*x^2)/_
+ (a^(2/3)*(b*c-a*d))+1/6*d^(2/3)*log(c^(2/3)-c^(1/3)*d^(1/3)*x+_
+ d^(2/3)*x^2)/(c^(2/3)*(b*c-a*d))-b^(2/3)*atan((a^(1/3)-_
+ 2*b^(1/3)*x)/(a^(1/3)*sqrt(3)))/(a^(2/3)*(b*c-a*d)*sqrt(3))+_
+ d^(2/3)*atan((c^(1/3)-2*d^(1/3)*x)/(c^(1/3)*sqrt(3)))/_
+ (c^(2/3)*(b*c-a*d)*sqrt(3))
+--R
+--R
+--R (2)
+--R +-+3+-+2 3+-+2 2 3+-+2 3+-+3+-+ 3+-+2
+--R - \|3 \|a \|d log(x \|d - x\|c \|d + \|c )
+--R +
+--R +-+3+-+2 3+-+2 3+-+ 3+-+
+--R 2\|3 \|a \|d log(x\|d + \|c )
+--R +
+--R +-+3+-+2 3+-+2 2 3+-+2 3+-+3+-+ 3+-+2
+--R \|3 \|b \|c log(x \|b - x\|a \|b + \|a )
+--R +
+--R 3+-+ 3+-+
+--R +-+3+-+2 3+-+2 3+-+ 3+-+ 3+-+2 3+-+2 2x\|d - \|c
+--R - 2\|3 \|b \|c log(x\|b + \|a + 6\|a \|d atan(-------------)
+--R +-+3+-+
+--R \|3 \|c
+--R +
+--R 3+-+ 3+-+
+--R 3+-+2 3+-+2 2x\|b - \|a
+--R - 6\|b \|c atan(-------------)
+--R +-+3+-+
+--R \|3 \|a
+--R /
+--R +-+3+-+2 3+-+2
+--R (6a d - 6b c)\|3 \|a \|c
+--R Type: Expression(Integer)
+--E 909
+
+--S 910 of 994
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +--+ +--+2 +--+
+--R | 2 | 2 | 2
+--R +-+ |d 2 |d |d 2 2
+--R - \|3 |-- log(c |-- - c d x |-- + d x )
+--R 3| 2 3| 2 3| 2
+--R \|c \|c \|c
+--R +
+--R +--+ +--+
+--R | 2 | 2
+--R +-+ |d |d
+--R 2\|3 |-- log(c |-- + d x)
+--R 3| 2 3| 2
+--R \|c \|c
+--R +
+--R +----+ +----+2 +----+
+--R | 2 | 2 | 2
+--R +-+ | b 2 | b | b 2 2
+--R - \|3 |- -- log(a |- -- + a b x |- -- + b x )
+--R 3| 2 3| 2 3| 2
+--R \| a \| a \| a
+--R +
+--R +----+
+--R | 2
+--R +-+ | b +-+
+--R +----+ +----+ +----+ a\|3 |- -- + 2b x\|3
+--R | 2 | 2 | 2 3| 2
+--R +-+ | b | b | b \| a
+--R 2\|3 |- -- log(- a |- -- + b x - 6 |- -- atan(-----------------------)
+--R 3| 2 3| 2 3| 2 +----+
+--R \| a \| a \| a | 2
+--R | b
+--R 3a |- --
+--R 3| 2
+--R \| a
+--R +
+--R +--+
+--R | 2
+--R +-+ |d +-+
+--R +--+ c\|3 |-- - 2d x\|3
+--R | 2 3| 2
+--R |d \|c
+--R - 6 |-- atan(---------------------)
+--R 3| 2 +--+
+--R \|c | 2
+--R |d
+--R 3c |--
+--R 3| 2
+--R \|c
+--R /
+--R +-+
+--R (6a d - 6b c)\|3
+--R Type: Union(Expression(Integer),...)
+--E 910
+
+--S 911 of 994
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +--+ +--+2 +--+
+--R | 2 | 2 | 2
+--R +-+3+-+2 3+-+2 |d 2 |d |d 2 2
+--R - \|3 \|a \|c |-- log(c |-- - c d x |-- + d x )
+--R 3| 2 3| 2 3| 2
+--R \|c \|c \|c
+--R +
+--R +--+ +--+
+--R | 2 | 2
+--R +-+3+-+2 3+-+2 |d |d
+--R 2\|3 \|a \|c |-- log(c |-- + d x)
+--R 3| 2 3| 2
+--R \|c \|c
+--R +
+--R +-+3+-+2 3+-+2 2 3+-+2 3+-+3+-+ 3+-+2
+--R \|3 \|a \|d log(x \|d - x\|c \|d + \|c )
+--R +
+--R +-+3+-+2 3+-+2 3+-+ 3+-+
+--R - 2\|3 \|a \|d log(x\|d + \|c )
+--R +
+--R +-+3+-+2 3+-+2 2 3+-+2 3+-+3+-+ 3+-+2
+--R - \|3 \|b \|c log(x \|b - x\|a \|b + \|a )
+--R +
+--R +-+3+-+2 3+-+2 3+-+ 3+-+
+--R 2\|3 \|b \|c log(x\|b + \|a )
+--R +
+--R +----+ +----+2 +----+
+--R | 2 | 2 | 2
+--R +-+ | b 3+-+2 3+-+2 2 | b | b 2 2
+--R - \|3 |- -- \|a \|c log(a |- -- + a b x |- -- + b x )
+--R 3| 2 3| 2 3| 2
+--R \| a \| a \| a
+--R +
+--R +----+ +----+
+--R | 2 | 2
+--R +-+ | b 3+-+2 3+-+2 | b
+--R 2\|3 |- -- \|a \|c log(- a |- -- + b x)
+--R 3| 2 3| 2
+--R \| a \| a
+--R +
+--R 3+-+ 3+-+ 3+-+ 3+-+
+--R 3+-+2 3+-+2 2x\|d - \|c 3+-+2 3+-+2 2x\|b - \|a
+--R - 6\|a \|d atan(------------- + 6\|b \|c atan(-------------)
+--R +-+3+-+ +-+3+-+
+--R \|3 \|c \|3 \|a
+--R +
+--R +----+
+--R | 2
+--R +-+ | b +-+
+--R +----+ a\|3 |- -- + 2b x\|3
+--R | 2 3| 2
+--R | b 3+-+2 3+-+2 \| a
+--R - 6 |- -- \|a \|c atan(-----------------------)
+--R 3| 2 +----+
+--R \| a | 2
+--R | b
+--R 3a |- --
+--R 3| 2
+--R \| a
+--R +
+--R +--+
+--R | 2
+--R +-+ |d +-+
+--R +--+ c\|3 |-- - 2d x\|3
+--R | 2 3| 2
+--R 3+-+2 3+-+2 |d \|c
+--R - 6\|a \|c |-- atan(---------------------)
+--R 3| 2 +--+
+--R \|c | 2
+--R |d
+--R 3c |--
+--R 3| 2
+--R \|c
+--R /
+--R +-+3+-+2 3+-+2
+--R (6a d - 6b c)\|3 \|a \|c
+--R Type: Expression(Integer)
+--E 911
+
+--S 912 of 994
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 912
+
+)clear all
+
+--S 913 of 994
+t0:=1/((a+b*x^3)*(c+d*x^3)^2)
+--R
+--R
+--R 1
+--R (1) -----------------------------------------------------
+--R 2 9 2 6 2 3 2
+--R b d x + (a d + 2b c d)x + (2a c d + b c )x + a c
+--R Type: Fraction(Polynomial(Integer))
+--E 913
+
+--S 914 of 994
+r0:=-1/3*d*x/(c*(b*c-a*d)*(c+d*x^3))+1/3*b^(5/3)*log(a^(1/3)+_
+ b^(1/3)*x)/(a^(2/3)*(b*c-a*d)^2)-1/9*d^(2/3)*(5*b*c-2*a*d)*_
+ log(c^(1/3)+d^(1/3)*x)/(c^(5/3)*(b*c-a*d)^2)-1/6*b^(5/3)*_
+ log(a^(2/3)-a^(1/3)*b^(1/3)*x+b^(2/3)*x^2)/(a^(2/3)*(b*c-_
+ a*d)^2)+1/18*d^(2/3)*(5*b*c-2*a*d)*log(c^(2/3)-c^(1/3)*_
+ d^(1/3)*x+d^(2/3)*x^2)/(c^(5/3)*(b*c-a*d)^2)-b^(5/3)*_
+ atan((a^(1/3)-2*b^(1/3)*x)/(a^(1/3)*sqrt(3)))/(a^(2/3)*_
+ (b*c-a*d)^2*sqrt(3))+1/3*d^(2/3)*(5*b*c-2*a*d)*atan((c^(1/3)-_
+ 2*d^(1/3)*x)/(c^(1/3)*sqrt(3)))/(c^(5/3)*(b*c-a*d)^2*sqrt(3))
+--R
+--R
+--R (2)
+--R 2 3 2 +-+3+-+2 3+-+2
+--R ((- 2a d + 5b c d)x - 2a c d + 5b c )\|3 \|a \|d
+--R *
+--R 2 3+-+2 3+-+3+-+ 3+-+2
+--R log(x \|d - x\|c \|d + \|c )
+--R +
+--R 2 3 2 +-+3+-+2 3+-+2 3+-+ 3+-+
+--R ((4a d - 10b c d)x + 4a c d - 10b c )\|3 \|a \|d log(x\|d + \|c )
+--R +
+--R 3 2 +-+3+-+2 3+-+2 2 3+-+2 3+-+3+-+ 3+-+2
+--R (- 3b c d x - 3b c )\|3 \|b \|c log(x \|b - x\|a \|b + \|a )
+--R +
+--R 3 2 +-+3+-+2 3+-+2 3+-+ 3+-+
+--R (6b c d x + 6b c )\|3 \|b \|c log(x\|b + \|a )
+--R +
+--R 3+-+ 3+-+
+--R 2 3 2 3+-+2 3+-+2 2x\|d - \|c
+--R ((12a d - 30b c d)x + 12a c d - 30b c )\|a \|d atan(-------------)
+--R +-+3+-+
+--R \|3 \|c
+--R +
+--R 3+-+ 3+-+
+--R 3 2 3+-+2 3+-+2 2x\|b - \|a
+--R (18b c d x + 18b c )\|b \|c atan(-------------)
+--R +-+3+-+
+--R \|3 \|a
+--R +
+--R 2 +-+3+-+2 3+-+2
+--R (6a d - 6b c d)x\|3 \|a \|c
+--R /
+--R 2 3 2 2 2 3 3 2 2 2 3 2 4 +-+
+--R ((18a c d - 36a b c d + 18b c d)x + 18a c d - 36a b c d + 18b c )\|3
+--R *
+--R 3+-+2 3+-+2
+--R \|a \|c
+--R Type: Expression(Integer)
+--E 914
+
+--S 915 of 994
+--a0:=integrate(t0,x)
+--E 915
+
+--S 916 of 994
+--m0:=a0-r0
+--E 916
+
+--S 917 of 994
+--d0:=D(m0,x)
+--E 917
+
+)clear all
+
+--S 918 of 994
+t0:=(c+d*x^3)^p/(a+b*x^3)^2
+--R
+--R
+--R 3 p
+--R (d x + c)
+--R (1) -------------------
+--R 2 6 3 2
+--R b x + 2a b x + a
+--R Type: Expression(Integer)
+--E 918
+
+--S 919 of 994
+--r0:=1/3*b*x*(c+d*x^3)^(1+p)/(a*(b*c-a*d)*(a+b*x^3))+1/3*(2*b*c-3*a*d)*_
+-- x*(c+d*x^3)^p*AppellF1(1/3,1,-p,4/3,-b*x^3/a,-d*x^3/c)/_
+-- (a^2*(b*c-a*d)*(1+d*x^3/c)^p)-1/12*b*d*(1+3*p)*x^4*(c+d*x^3)^p*_
+-- AppellF1(4/3,1,-p,7/3,-b*x^3/a,-d*x^3/c)/(a^2*(b*c-a*d)*(1+d*x^3/c)^p)
+--E 919
+
+--S 920 of 994
+--a0:=integrate(t0,x)
+--E 920
+
+--S 921 of 994
+--m0:=a0-r0
+--E 921
+
+--S 922 of 994
+--d0:=D(m0,x)
+--E 922
+
+)clear all
+
+--S 923 of 994
+t0:=(c+d*x^3)^5/(a+b*x^3)^2
+--R
+--R
+--R 5 15 4 12 2 3 9 3 2 6 4 3 5
+--R d x + 5c d x + 10c d x + 10c d x + 5c d x + c
+--R (1) -----------------------------------------------------
+--R 2 6 3 2
+--R b x + 2a b x + a
+--R Type: Fraction(Polynomial(Integer))
+--E 923
+
+--S 924 of 994
+r0:=d^2*(10*b^3*c^3-20*a*b^2*c^2*d+15*a^2*b*c*d^2-4*a^3*d^3)*x/b^5+_
+ 1/4*d^3*(10*b^2*c^2-10*a*b*c*d+3*a^2*d^2)*x^4/b^4+1/7*d^4*_
+ (5*b*c-2*a*d)*x^7/b^3+1/10*d^5*x^10/b^2+1/3*(b*c-a*d)^5*x/_
+ (a*b^5*(a+b*x^3))+1/9*(b*c-a*d)^4*(2*b*c+13*a*d)*log(a^(1/3)+_
+ b^(1/3)*x)/(a^(5/3)*b^(16/3))-1/18*(b*c-a*d)^4*(2*b*c+13*a*d)*_
+ log(a^(2/3)-a^(1/3)*b^(1/3)*x+b^(2/3)*x^2)/(a^(5/3)*b^(16/3))-_
+ 1/3*(b*c-a*d)^4*(2*b*c+13*a*d)*atan((a^(1/3)-2*b^(1/3)*x)/_
+ (a^(1/3)*sqrt(3)))/(a^(5/3)*b^(16/3)*sqrt(3))
+--R
+--R
+--R (2)
+--R 5 5 4 2 4 3 3 2 3 2 4 3 2
+--R - 910a b d + 3500a b c d - 4900a b c d + 2800a b c d
+--R +
+--R 5 4 6 5
+--R - 350a b c d - 140b c
+--R *
+--R 3
+--R x
+--R +
+--R 6 5 5 4 4 2 2 3 3 3 3 2 2 4 4
+--R - 910a d + 3500a b c d - 4900a b c d + 2800a b c d - 350a b c d
+--R +
+--R 5 5
+--R - 140a b c
+--R *
+--R +-+ 2 3+-+2 3+-+3+-+ 3+-+2
+--R \|3 log(x \|b - x\|a \|b + \|a )
+--R +
+--R 5 5 4 2 4 3 3 2 3 2 4 3 2
+--R 1820a b d - 7000a b c d + 9800a b c d - 5600a b c d
+--R +
+--R 5 4 6 5
+--R 700a b c d + 280b c
+--R *
+--R 3
+--R x
+--R +
+--R 6 5 5 4 4 2 2 3 3 3 3 2 2 4 4
+--R 1820a d - 7000a b c d + 9800a b c d - 5600a b c d + 700a b c d
+--R +
+--R 5 5
+--R 280a b c
+--R *
+--R +-+ 3+-+ 3+-+
+--R \|3 log(x\|b + \|a )
+--R +
+--R 5 5 4 2 4 3 3 2 3 2 4 3 2
+--R 5460a b d - 21000a b c d + 29400a b c d - 16800a b c d
+--R +
+--R 5 4 6 5
+--R 2100a b c d + 840b c
+--R *
+--R 3
+--R x
+--R +
+--R 6 5 5 4 4 2 2 3 3 3 3 2
+--R 5460a d - 21000a b c d + 29400a b c d - 16800a b c d
+--R +
+--R 2 4 4 5 5
+--R 2100a b c d + 840a b c
+--R *
+--R 3+-+ 3+-+
+--R 2x\|b - \|a
+--R atan(-------------)
+--R +-+3+-+
+--R \|3 \|a
+--R +
+--R 4 5 13 2 3 5 4 4 10
+--R 126a b d x + (- 234a b d + 900a b c d )x
+--R +
+--R 3 2 5 2 3 4 4 2 3 7
+--R (585a b d - 2250a b c d + 3150a b c d )x
+--R +
+--R 4 5 3 2 4 2 3 2 3 4 3 2 4
+--R (- 4095a b d + 15750a b c d - 22050a b c d + 12600a b c d )x
+--R +
+--R 5 5 4 4 3 2 2 3 2 3 3 2
+--R - 5460a d + 21000a b c d - 29400a b c d + 16800a b c d
+--R +
+--R 4 4 5 5
+--R - 2100a b c d + 420b c
+--R *
+--R x
+--R *
+--R +-+3+-+2 3+-+
+--R \|3 \|a \|b
+--R /
+--R 6 3 2 5 +-+3+-+2 3+-+
+--R (1260a b x + 1260a b )\|3 \|a \|b
+--R Type: Expression(Integer)
+--E 924
+
+--S 925 of 994
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 5 5 4 2 4 3 3 2 3 2 4 3 2
+--R - 910a b d + 3500a b c d - 4900a b c d + 2800a b c d
+--R +
+--R 5 4 6 5
+--R - 350a b c d - 140b c
+--R *
+--R 3
+--R x
+--R +
+--R 6 5 5 4 4 2 2 3 3 3 3 2 2 4 4
+--R - 910a d + 3500a b c d - 4900a b c d + 2800a b c d - 350a b c d
+--R +
+--R 5 5
+--R - 140a b c
+--R *
+--R +---+2 +---+
+--R +-+ 2 3| 2 3| 2 2
+--R \|3 log(x \|a b - a x\|a b + a )
+--R +
+--R 5 5 4 2 4 3 3 2 3 2 4 3 2
+--R 1820a b d - 7000a b c d + 9800a b c d - 5600a b c d
+--R +
+--R 5 4 6 5
+--R 700a b c d + 280b c
+--R *
+--R 3
+--R x
+--R +
+--R 6 5 5 4 4 2 2 3 3 3 3 2 2 4 4
+--R 1820a d - 7000a b c d + 9800a b c d - 5600a b c d + 700a b c d
+--R +
+--R 5 5
+--R 280a b c
+--R *
+--R +---+
+--R +-+ 3| 2
+--R \|3 log(x\|a b + a)
+--R +
+--R 5 5 4 2 4 3 3 2 3 2 4 3 2
+--R 5460a b d - 21000a b c d + 29400a b c d - 16800a b c d
+--R +
+--R 5 4 6 5
+--R 2100a b c d + 840b c
+--R *
+--R 3
+--R x
+--R +
+--R 6 5 5 4 4 2 2 3 3 3 3 2
+--R 5460a d - 21000a b c d + 29400a b c d - 16800a b c d
+--R +
+--R 2 4 4 5 5
+--R 2100a b c d + 840a b c
+--R *
+--R +---+
+--R +-+3| 2 +-+
+--R 2x\|3 \|a b - a\|3
+--R atan(--------------------)
+--R 3a
+--R +
+--R 4 5 13 2 3 5 4 4 10
+--R 126a b d x + (- 234a b d + 900a b c d )x
+--R +
+--R 3 2 5 2 3 4 4 2 3 7
+--R (585a b d - 2250a b c d + 3150a b c d )x
+--R +
+--R 4 5 3 2 4 2 3 2 3 4 3 2 4
+--R (- 4095a b d + 15750a b c d - 22050a b c d + 12600a b c d )x
+--R +
+--R 5 5 4 4 3 2 2 3 2 3 3 2
+--R - 5460a d + 21000a b c d - 29400a b c d + 16800a b c d
+--R +
+--R 4 4 5 5
+--R - 2100a b c d + 420b c
+--R *
+--R x
+--R *
+--R +---+
+--R +-+3| 2
+--R \|3 \|a b
+--R /
+--R +---+
+--R 6 3 2 5 +-+3| 2
+--R (1260a b x + 1260a b )\|3 \|a b
+--R Type: Union(Expression(Integer),...)
+--E 925
+
+--S 926 of 994
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R 5 5 4 4 3 2 2 3 2 3 3 2 4 4 5 5
+--R (- 13a d + 50a b c d - 70a b c d + 40a b c d - 5a b c d - 2b c )
+--R *
+--R +---+2 +---+
+--R +-+3+-+2 3+-+ 2 3| 2 3| 2 2
+--R \|3 \|a \|b log(x \|a b - a x\|a b + a )
+--R +
+--R 5 5 4 4 3 2 2 3 2 3 3 2 4 4 5 5
+--R (26a d - 100a b c d + 140a b c d - 80a b c d + 10a b c d + 4b c )
+--R *
+--R +---+
+--R +-+3+-+2 3+-+ 3| 2
+--R \|3 \|a \|b log(x\|a b + a)
+--R +
+--R 5 5 4 4 3 2 2 3 2 3 3 2 4 4 5 5 +-+
+--R (13a d - 50a b c d + 70a b c d - 40a b c d + 5a b c d + 2b c )\|3
+--R *
+--R +---+
+--R 3| 2 2 3+-+2 3+-+3+-+ 3+-+2
+--R \|a b log(x \|b - x\|a \|b + \|a )
+--R +
+--R 5 5 4 4 3 2 2 3 2 3 3 2 4 4 5 5
+--R (- 26a d + 100a b c d - 140a b c d + 80a b c d - 10a b c d - 4b c )
+--R *
+--R +---+
+--R +-+3| 2 3+-+ 3+-+
+--R \|3 \|a b log(x\|b + \|a )
+--R +
+--R 5 5 4 4 3 2 2 3 2 3 3 2 4 4 5 5
+--R (78a d - 300a b c d + 420a b c d - 240a b c d + 30a b c d + 12b c )
+--R *
+--R +---+
+--R +-+3| 2 +-+
+--R 3+-+2 3+-+ 2x\|3 \|a b - a\|3
+--R \|a \|b atan(--------------------)
+--R 3a
+--R +
+--R 5 5 4 4 3 2 2 3 2 3 3 2 4 4
+--R - 78a d + 300a b c d - 420a b c d + 240a b c d - 30a b c d
+--R +
+--R 5 5
+--R - 12b c
+--R *
+--R +---+ 3+-+ 3+-+
+--R 3| 2 2x\|b - \|a
+--R \|a b atan(-------------)
+--R +-+3+-+
+--R \|3 \|a
+--R /
+--R +---+
+--R 5 +-+3+-+2 3+-+3| 2
+--R 18a b \|3 \|a \|b \|a b
+--R Type: Expression(Integer)
+--E 926
+
+--S 927 of 994
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 927
+
+)clear all
+
+--S 928 of 994
+t0:=(c+d*x^3)^4/(a+b*x^3)^2
+--R
+--R
+--R 4 12 3 9 2 2 6 3 3 4
+--R d x + 4c d x + 6c d x + 4c d x + c
+--R (1) ----------------------------------------
+--R 2 6 3 2
+--R b x + 2a b x + a
+--R Type: Fraction(Polynomial(Integer))
+--E 928
+
+--S 929 of 994
+r0:=d^2*(6*b^2*c^2-8*a*b*c*d+3*a^2*d^2)*x/b^4+1/2*d^3*(2*b*c-a*d)*_
+ x^4/b^3+1/7*d^4*x^7/b^2+1/3*(b*c-a*d)^4*x/(a*b^4*(a+b*x^3))+_
+ 2/9*(b*c-a*d)^3*(b*c+5*a*d)*log(a^(1/3)+b^(1/3)*x)/(a^(5/3)*_
+ b^(13/3))-1/9*(b*c-a*d)^3*(b*c+5*a*d)*log(a^(2/3)-a^(1/3)*_
+ b^(1/3)*x+b^(2/3)*x^2)/(a^(5/3)*b^(13/3))-2/3*(b*c-a*d)^3*_
+ (b*c+5*a*d)*atan((a^(1/3)-2*b^(1/3)*x)/(a^(1/3)*sqrt(3)))/_
+ (a^(5/3)*b^(13/3)*sqrt(3))
+--R
+--R
+--R (2)
+--R 4 4 3 2 3 2 3 2 2 4 3 5 4 3
+--R (70a b d - 196a b c d + 168a b c d - 28a b c d - 14b c )x
+--R +
+--R 5 4 4 3 3 2 2 2 2 3 3 4 4
+--R 70a d - 196a b c d + 168a b c d - 28a b c d - 14a b c
+--R *
+--R +-+ 2 3+-+2 3+-+3+-+ 3+-+2
+--R \|3 log(x \|b - x\|a \|b + \|a )
+--R +
+--R 4 4 3 2 3 2 3 2 2 4 3 5 4 3
+--R (- 140a b d + 392a b c d - 336a b c d + 56a b c d + 28b c )x
+--R +
+--R 5 4 4 3 3 2 2 2 2 3 3 4 4
+--R - 140a d + 392a b c d - 336a b c d + 56a b c d + 28a b c
+--R *
+--R +-+ 3+-+ 3+-+
+--R \|3 log(x\|b + \|a )
+--R +
+--R 4 4 3 2 3 2 3 2 2 4 3 5 4 3
+--R (- 420a b d + 1176a b c d - 1008a b c d + 168a b c d + 84b c )x
+--R +
+--R 5 4 4 3 3 2 2 2 2 3 3 4 4
+--R - 420a d + 1176a b c d - 1008a b c d + 168a b c d + 84a b c
+--R *
+--R 3+-+ 3+-+
+--R 2x\|b - \|a
+--R atan(-------------)
+--R +-+3+-+
+--R \|3 \|a
+--R +
+--R 3 4 10 2 2 4 3 3 7
+--R 18a b d x + (- 45a b d + 126a b c d )x
+--R +
+--R 3 4 2 2 3 3 2 2 4
+--R (315a b d - 882a b c d + 756a b c d )x
+--R +
+--R 4 4 3 3 2 2 2 2 3 3 4 4
+--R (420a d - 1176a b c d + 1008a b c d - 168a b c d + 42b c )x
+--R *
+--R +-+3+-+2 3+-+
+--R \|3 \|a \|b
+--R /
+--R 5 3 2 4 +-+3+-+2 3+-+
+--R (126a b x + 126a b )\|3 \|a \|b
+--R Type: Expression(Integer)
+--E 929
+
+--S 930 of 994
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 4 4 3 2 3 2 3 2 2 4 3 5 4 3
+--R (- 70a b d + 196a b c d - 168a b c d + 28a b c d + 14b c )x
+--R +
+--R 5 4 4 3 3 2 2 2 2 3 3 4 4
+--R - 70a d + 196a b c d - 168a b c d + 28a b c d + 14a b c
+--R *
+--R +-----+2 +-----+
+--R +-+ 2 3| 2 3| 2 2
+--R \|3 log(x \|- a b + a x\|- a b + a )
+--R +
+--R 4 4 3 2 3 2 3 2 2 4 3 5 4 3
+--R (140a b d - 392a b c d + 336a b c d - 56a b c d - 28b c )x
+--R +
+--R 5 4 4 3 3 2 2 2 2 3 3 4 4
+--R 140a d - 392a b c d + 336a b c d - 56a b c d - 28a b c
+--R *
+--R +-----+
+--R +-+ 3| 2
+--R \|3 log(x\|- a b - a)
+--R +
+--R 4 4 3 2 3 2 3 2 2 4 3 5 4 3
+--R (- 420a b d + 1176a b c d - 1008a b c d + 168a b c d + 84b c )x
+--R +
+--R 5 4 4 3 3 2 2 2 2 3 3 4 4
+--R - 420a d + 1176a b c d - 1008a b c d + 168a b c d + 84a b c
+--R *
+--R +-----+
+--R +-+3| 2 +-+
+--R 2x\|3 \|- a b + a\|3
+--R atan(----------------------)
+--R 3a
+--R +
+--R 3 4 10 2 2 4 3 3 7
+--R 18a b d x + (- 45a b d + 126a b c d )x
+--R +
+--R 3 4 2 2 3 3 2 2 4
+--R (315a b d - 882a b c d + 756a b c d )x
+--R +
+--R 4 4 3 3 2 2 2 2 3 3 4 4
+--R (420a d - 1176a b c d + 1008a b c d - 168a b c d + 42b c )x
+--R *
+--R +-----+
+--R +-+3| 2
+--R \|3 \|- a b
+--R /
+--R +-----+
+--R 5 3 2 4 +-+3| 2
+--R (126a b x + 126a b )\|3 \|- a b
+--R Type: Union(Expression(Integer),...)
+--E 930
+
+--S 931 of 994
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +-----+
+--R 4 4 3 3 2 2 2 2 3 3 4 4 +-+3| 2
+--R (- 5a d + 14a b c d - 12a b c d + 2a b c d + b c )\|3 \|- a b
+--R *
+--R 2 3+-+2 3+-+3+-+ 3+-+2
+--R log(x \|b - x\|a \|b + \|a )
+--R +
+--R +-----+
+--R 4 4 3 3 2 2 2 2 3 3 4 4 +-+3| 2
+--R (10a d - 28a b c d + 24a b c d - 4a b c d - 2b c )\|3 \|- a b
+--R *
+--R 3+-+ 3+-+
+--R log(x\|b + \|a )
+--R +
+--R 4 4 3 3 2 2 2 2 3 3 4 4 +-+3+-+2 3+-+
+--R (- 5a d + 14a b c d - 12a b c d + 2a b c d + b c )\|3 \|a \|b
+--R *
+--R +-----+2 +-----+
+--R 2 3| 2 3| 2 2
+--R log(x \|- a b + a x\|- a b + a )
+--R +
+--R 4 4 3 3 2 2 2 2 3 3 4 4 +-+3+-+2 3+-+
+--R (10a d - 28a b c d + 24a b c d - 4a b c d - 2b c )\|3 \|a \|b
+--R *
+--R +-----+
+--R 3| 2
+--R log(x\|- a b - a)
+--R +
+--R +-----+
+--R 4 4 3 3 2 2 2 2 3 3 4 4 3| 2
+--R (30a d - 84a b c d + 72a b c d - 12a b c d - 6b c )\|- a b
+--R *
+--R 3+-+ 3+-+
+--R 2x\|b - \|a
+--R atan(-------------)
+--R +-+3+-+
+--R \|3 \|a
+--R +
+--R 4 4 3 3 2 2 2 2 3 3 4 4 3+-+2 3+-+
+--R (- 30a d + 84a b c d - 72a b c d + 12a b c d + 6b c )\|a \|b
+--R *
+--R +-----+
+--R +-+3| 2 +-+
+--R 2x\|3 \|- a b + a\|3
+--R atan(----------------------)
+--R 3a
+--R /
+--R +-----+
+--R 4 +-+3| 2 3+-+2 3+-+
+--R 9a b \|3 \|- a b \|a \|b
+--R Type: Expression(Integer)
+--E 931
+
+--S 932 of 994
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 932
+
+)clear all
+
+--S 933 of 994
+t0:=(c+d*x^3)^3/(a+b*x^3)^2
+--R
+--R
+--R 3 9 2 6 2 3 3
+--R d x + 3c d x + 3c d x + c
+--R (1) -----------------------------
+--R 2 6 3 2
+--R b x + 2a b x + a
+--R Type: Fraction(Polynomial(Integer))
+--E 933
+
+--S 934 of 994
+r0:=d^2*(3*b*c-2*a*d)*x/b^3+1/4*d^3*x^4/b^2+1/3*(b*c-a*d)^3*_
+ x/(a*b^3*(a+b*x^3))+1/9*(b*c-a*d)^2*(2*b*c+7*a*d)*_
+ log(a^(1/3)+b^(1/3)*x)/(a^(5/3)*b^(10/3))-1/18*(b*c-a*d)^2*_
+ (2*b*c+7*a*d)*log(a^(2/3)-a^(1/3)*b^(1/3)*x+b^(2/3)*x^2)/_
+ (a^(5/3)*b^(10/3))-1/3*(b*c-a*d)^2*(2*b*c+7*a*d)*_
+ atan((a^(1/3)-2*b^(1/3)*x)/(a^(1/3)*sqrt(3)))/(a^(5/3)*b^(10/3)*sqrt(3))
+--R
+--R
+--R (2)
+--R 3 3 2 2 2 3 2 4 3 3 4 3 3 2
+--R (- 14a b d + 24a b c d - 6a b c d - 4b c )x - 14a d + 24a b c d
+--R +
+--R 2 2 2 3 3
+--R - 6a b c d - 4a b c
+--R *
+--R +-+ 2 3+-+2 3+-+3+-+ 3+-+2
+--R \|3 log(x \|b - x\|a \|b + \|a )
+--R +
+--R 3 3 2 2 2 3 2 4 3 3 4 3 3 2
+--R (28a b d - 48a b c d + 12a b c d + 8b c )x + 28a d - 48a b c d
+--R +
+--R 2 2 2 3 3
+--R 12a b c d + 8a b c
+--R *
+--R +-+ 3+-+ 3+-+
+--R \|3 log(x\|b + \|a )
+--R +
+--R 3 3 2 2 2 3 2 4 3 3 4 3
+--R (84a b d - 144a b c d + 36a b c d + 24b c )x + 84a d
+--R +
+--R 3 2 2 2 2 3 3
+--R - 144a b c d + 36a b c d + 24a b c
+--R *
+--R 3+-+ 3+-+
+--R 2x\|b - \|a
+--R atan(-------------)
+--R +-+3+-+
+--R \|3 \|a
+--R +
+--R 2 3 7 2 3 2 2 4
+--R 9a b d x + (- 63a b d + 108a b c d )x
+--R +
+--R 3 3 2 2 2 2 3 3
+--R (- 84a d + 144a b c d - 36a b c d + 12b c )x
+--R *
+--R +-+3+-+2 3+-+
+--R \|3 \|a \|b
+--R /
+--R 4 3 2 3 +-+3+-+2 3+-+
+--R (36a b x + 36a b )\|3 \|a \|b
+--R Type: Expression(Integer)
+--E 934
+
+--S 935 of 994
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 3 3 2 2 2 3 2 4 3 3 4 3 3 2
+--R (- 14a b d + 24a b c d - 6a b c d - 4b c )x - 14a d + 24a b c d
+--R +
+--R 2 2 2 3 3
+--R - 6a b c d - 4a b c
+--R *
+--R +---+2 +---+
+--R +-+ 2 3| 2 3| 2 2
+--R \|3 log(x \|a b - a x\|a b + a )
+--R +
+--R 3 3 2 2 2 3 2 4 3 3 4 3 3 2
+--R (28a b d - 48a b c d + 12a b c d + 8b c )x + 28a d - 48a b c d
+--R +
+--R 2 2 2 3 3
+--R 12a b c d + 8a b c
+--R *
+--R +---+
+--R +-+ 3| 2
+--R \|3 log(x\|a b + a)
+--R +
+--R 3 3 2 2 2 3 2 4 3 3 4 3
+--R (84a b d - 144a b c d + 36a b c d + 24b c )x + 84a d
+--R +
+--R 3 2 2 2 2 3 3
+--R - 144a b c d + 36a b c d + 24a b c
+--R *
+--R +---+
+--R +-+3| 2 +-+
+--R 2x\|3 \|a b - a\|3
+--R atan(--------------------)
+--R 3a
+--R +
+--R 2 3 7 2 3 2 2 4
+--R 9a b d x + (- 63a b d + 108a b c d )x
+--R +
+--R 3 3 2 2 2 2 3 3
+--R (- 84a d + 144a b c d - 36a b c d + 12b c )x
+--R *
+--R +---+
+--R +-+3| 2
+--R \|3 \|a b
+--R /
+--R +---+
+--R 4 3 2 3 +-+3| 2
+--R (36a b x + 36a b )\|3 \|a b
+--R Type: Union(Expression(Integer),...)
+--E 935
+
+--S 936 of 994
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R 3 3 2 2 2 2 3 3 +-+3+-+2 3+-+
+--R (- 7a d + 12a b c d - 3a b c d - 2b c )\|3 \|a \|b
+--R *
+--R +---+2 +---+
+--R 2 3| 2 3| 2 2
+--R log(x \|a b - a x\|a b + a )
+--R +
+--R +---+
+--R 3 3 2 2 2 2 3 3 +-+3+-+2 3+-+ 3| 2
+--R (14a d - 24a b c d + 6a b c d + 4b c )\|3 \|a \|b log(x\|a b + a)
+--R +
+--R +---+
+--R 3 3 2 2 2 2 3 3 +-+3| 2
+--R (7a d - 12a b c d + 3a b c d + 2b c )\|3 \|a b
+--R *
+--R 2 3+-+2 3+-+3+-+ 3+-+2
+--R log(x \|b - x\|a \|b + \|a )
+--R +
+--R +---+
+--R 3 3 2 2 2 2 3 3 +-+3| 2 3+-+ 3+-+
+--R (- 14a d + 24a b c d - 6a b c d - 4b c )\|3 \|a b log(x\|b + \|a )
+--R +
+--R 3 3 2 2 2 2 3 3 3+-+2 3+-+
+--R (42a d - 72a b c d + 18a b c d + 12b c )\|a \|b
+--R *
+--R +---+
+--R +-+3| 2 +-+
+--R 2x\|3 \|a b - a\|3
+--R atan(--------------------)
+--R 3a
+--R +
+--R +---+ 3+-+ 3+-+
+--R 3 3 2 2 2 2 3 3 3| 2 2x\|b - \|a
+--R (- 42a d + 72a b c d - 18a b c d - 12b c )\|a b atan(-------------)
+--R +-+3+-+
+--R \|3 \|a
+--R /
+--R +---+
+--R 3 +-+3+-+2 3+-+3| 2
+--R 18a b \|3 \|a \|b \|a b
+--R Type: Expression(Integer)
+--E 936
+
+--S 937 of 994
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 937
+
+)clear all
+
+--S 938 of 994
+t0:=(c+d*x^3)^2/(a+b*x^3)^2
+--R
+--R
+--R 2 6 3 2
+--R d x + 2c d x + c
+--R (1) -------------------
+--R 2 6 3 2
+--R b x + 2a b x + a
+--R Type: Fraction(Polynomial(Integer))
+--E 938
+
+--S 939 of 994
+r0:=d^2*x/b^2+1/3*(b*c-a*d)^2*x/(a*b^2*(a+b*x^3))+2/9*(b*c-a*d)*_
+ (b*c+2*a*d)*log(a^(1/3)+b^(1/3)*x)/(a^(5/3)*b^(7/3))-_
+ 1/9*(b*c-a*d)*(b*c+2*a*d)*log(a^(2/3)-a^(1/3)*b^(1/3)*x+_
+ b^(2/3)*x^2)/(a^(5/3)*b^(7/3))-2/3*(b*c-a*d)*(b*c+2*a*d)*_
+ atan((a^(1/3)-2*b^(1/3)*x)/(a^(1/3)*sqrt(3)))/(a^(5/3)*b^(7/3)*sqrt(3))
+--R
+--R
+--R (2)
+--R 2 2 2 3 2 3 3 2 2 2 2 +-+
+--R ((2a b d - a b c d - b c )x + 2a d - a b c d - a b c )\|3
+--R *
+--R 2 3+-+2 3+-+3+-+ 3+-+2
+--R log(x \|b - x\|a \|b + \|a )
+--R +
+--R 2 2 2 3 2 3 3 2 2 2 2 +-+
+--R ((- 4a b d + 2a b c d + 2b c )x - 4a d + 2a b c d + 2a b c )\|3
+--R *
+--R 3+-+ 3+-+
+--R log(x\|b + \|a )
+--R +
+--R 2 2 2 3 2 3 3 2 2 2 2
+--R ((- 12a b d + 6a b c d + 6b c )x - 12a d + 6a b c d + 6a b c )
+--R *
+--R 3+-+ 3+-+
+--R 2x\|b - \|a
+--R atan(-------------)
+--R +-+3+-+
+--R \|3 \|a
+--R +
+--R 2 4 2 2 2 2 +-+3+-+2 3+-+
+--R (9a b d x + (12a d - 6a b c d + 3b c )x)\|3 \|a \|b
+--R /
+--R 3 3 2 2 +-+3+-+2 3+-+
+--R (9a b x + 9a b )\|3 \|a \|b
+--R Type: Expression(Integer)
+--E 939
+
+--S 940 of 994
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 2 2 2 3 2 3 3 2 2 2 2 +-+
+--R ((- 2a b d + a b c d + b c )x - 2a d + a b c d + a b c )\|3
+--R *
+--R +-----+2 +-----+
+--R 2 3| 2 3| 2 2
+--R log(x \|- a b + a x\|- a b + a )
+--R +
+--R 2 2 2 3 2 3 3 2 2 2 2 +-+
+--R ((4a b d - 2a b c d - 2b c )x + 4a d - 2a b c d - 2a b c )\|3
+--R *
+--R +-----+
+--R 3| 2
+--R log(x\|- a b - a)
+--R +
+--R 2 2 2 3 2 3 3 2 2 2 2
+--R ((- 12a b d + 6a b c d + 6b c )x - 12a d + 6a b c d + 6a b c )
+--R *
+--R +-----+
+--R +-+3| 2 +-+
+--R 2x\|3 \|- a b + a\|3
+--R atan(----------------------)
+--R 3a
+--R +
+--R +-----+
+--R 2 4 2 2 2 2 +-+3| 2
+--R (9a b d x + (12a d - 6a b c d + 3b c )x)\|3 \|- a b
+--R /
+--R +-----+
+--R 3 3 2 2 +-+3| 2
+--R (9a b x + 9a b )\|3 \|- a b
+--R Type: Union(Expression(Integer),...)
+--E 940
+
+--S 941 of 994
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +-----+
+--R 2 2 2 2 +-+3| 2 2 3+-+2 3+-+3+-+ 3+-+2
+--R (- 2a d + a b c d + b c )\|3 \|- a b log(x \|b - x\|a \|b + \|a )
+--R +
+--R +-----+
+--R 2 2 2 2 +-+3| 2 3+-+ 3+-+
+--R (4a d - 2a b c d - 2b c )\|3 \|- a b log(x\|b + \|a )
+--R +
+--R 2 2 2 2 +-+3+-+2 3+-+
+--R (- 2a d + a b c d + b c )\|3 \|a \|b
+--R *
+--R +-----+2 +-----+
+--R 2 3| 2 3| 2 2
+--R log(x \|- a b + a x\|- a b + a )
+--R +
+--R +-----+
+--R 2 2 2 2 +-+3+-+2 3+-+ 3| 2
+--R (4a d - 2a b c d - 2b c )\|3 \|a \|b log(x\|- a b - a)
+--R +
+--R +-----+ 3+-+ 3+-+
+--R 2 2 2 2 3| 2 2x\|b - \|a
+--R (12a d - 6a b c d - 6b c )\|- a b atan(-------------)
+--R +-+3+-+
+--R \|3 \|a
+--R +
+--R +-----+
+--R +-+3| 2 +-+
+--R 2 2 2 2 3+-+2 3+-+ 2x\|3 \|- a b + a\|3
+--R (- 12a d + 6a b c d + 6b c )\|a \|b atan(----------------------)
+--R 3a
+--R /
+--R +-----+
+--R 2 +-+3| 2 3+-+2 3+-+
+--R 9a b \|3 \|- a b \|a \|b
+--R Type: Expression(Integer)
+--E 941
+
+--S 942 of 994
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 942
+
+)clear all
+
+--S 943 of 994
+t0:=(c+d*x^3)/(a+b*x^3)^2
+--R
+--R
+--R 3
+--R d x + c
+--R (1) -------------------
+--R 2 6 3 2
+--R b x + 2a b x + a
+--R Type: Fraction(Polynomial(Integer))
+--E 943
+
+--S 944 of 994
+r0:=1/3*(b*c-a*d)*x/(a*b*(a+b*x^3))+1/9*(2*b*c+a*d)*log(a^(1/3)+_
+ b^(1/3)*x)/(a^(5/3)*b^(4/3))-1/18*(2*b*c+a*d)*log(a^(2/3)-_
+ a^(1/3)*b^(1/3)*x+b^(2/3)*x^2)/(a^(5/3)*b^(4/3))-1/3*(2*b*c+_
+ a*d)*atan((a^(1/3)-2*b^(1/3)*x)/(a^(1/3)*sqrt(3)))/(a^(5/3)*_
+ b^(4/3)*sqrt(3))
+--R
+--R
+--R (2)
+--R 2 3 2 +-+ 2 3+-+2 3+-+3+-+ 3+-+2
+--R ((- a b d - 2b c)x - a d - 2a b c)\|3 log(x \|b - x\|a \|b + \|a )
+--R +
+--R 2 3 2 +-+ 3+-+ 3+-+
+--R ((2a b d + 4b c)x + 2a d + 4a b c)\|3 log(x\|b + \|a )
+--R +
+--R 3+-+ 3+-+
+--R 2 3 2 2x\|b - \|a
+--R ((6a b d + 12b c)x + 6a d + 12a b c)atan(-------------)
+--R +-+3+-+
+--R \|3 \|a
+--R +
+--R +-+3+-+2 3+-+
+--R (- 6a d + 6b c)x\|3 \|a \|b
+--R /
+--R 2 3 2 +-+3+-+2 3+-+
+--R (18a b x + 18a b)\|3 \|a \|b
+--R Type: Expression(Integer)
+--E 944
+
+--S 945 of 994
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +---+2 +---+
+--R 2 3 2 +-+ 2 3| 2 3| 2 2
+--R ((- a b d - 2b c)x - a d - 2a b c)\|3 log(x \|a b - a x\|a b + a )
+--R +
+--R +---+
+--R 2 3 2 +-+ 3| 2
+--R ((2a b d + 4b c)x + 2a d + 4a b c)\|3 log(x\|a b + a)
+--R +
+--R +---+
+--R +-+3| 2 +-+
+--R 2 3 2 2x\|3 \|a b - a\|3
+--R ((6a b d + 12b c)x + 6a d + 12a b c)atan(--------------------)
+--R 3a
+--R +
+--R +---+
+--R +-+3| 2
+--R (- 6a d + 6b c)x\|3 \|a b
+--R /
+--R +---+
+--R 2 3 2 +-+3| 2
+--R (18a b x + 18a b)\|3 \|a b
+--R Type: Union(Expression(Integer),...)
+--E 945
+
+--S 946 of 994
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +---+2 +---+
+--R +-+3+-+2 3+-+ 2 3| 2 3| 2 2
+--R (- a d - 2b c)\|3 \|a \|b log(x \|a b - a x\|a b + a )
+--R +
+--R +---+
+--R +-+3+-+2 3+-+ 3| 2
+--R (2a d + 4b c)\|3 \|a \|b log(x\|a b + a)
+--R +
+--R +---+
+--R +-+3| 2 2 3+-+2 3+-+3+-+ 3+-+2
+--R (a d + 2b c)\|3 \|a b log(x \|b - x\|a \|b + \|a )
+--R +
+--R +---+
+--R +-+3| 2 3+-+ 3+-+
+--R (- 2a d - 4b c)\|3 \|a b log(x\|b + \|a )
+--R +
+--R +---+
+--R +-+3| 2 +-+
+--R 3+-+2 3+-+ 2x\|3 \|a b - a\|3
+--R (6a d + 12b c)\|a \|b atan(--------------------)
+--R 3a
+--R +
+--R +---+ 3+-+ 3+-+
+--R 3| 2 2x\|b - \|a
+--R (- 6a d - 12b c)\|a b atan(-------------)
+--R +-+3+-+
+--R \|3 \|a
+--R /
+--R +---+
+--R +-+3+-+2 3+-+3| 2
+--R 18a b\|3 \|a \|b \|a b
+--R Type: Expression(Integer)
+--E 946
+
+--S 947 of 994
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 947
+
+)clear all
+
+--S 948 of 994
+t0:=1/((a+b*x^3)^2*(c+d*x^3))
+--R
+--R
+--R 1
+--R (1) --------------------------------------------------
+--R 2 9 2 6 2 3 2
+--R b d x + (2a b d + b c)x + (a d + 2a b c)x + a c
+--R Type: Fraction(Polynomial(Integer))
+--E 948
+
+--S 949 of 994
+r0:=1/3*b*x/(a*(b*c-a*d)*(a+b*x^3))+1/9*b^(2/3)*(2*b*c-5*a*d)*_
+ log(a^(1/3)+b^(1/3)*x)/(a^(5/3)*(b*c-a*d)^2)+1/3*d^(5/3)*_
+ log(c^(1/3)+d^(1/3)*x)/(c^(2/3)*(b*c-a*d)^2)-1/18*b^(2/3)*_
+ (2*b*c-5*a*d)*log(a^(2/3)-a^(1/3)*b^(1/3)*x+b^(2/3)*x^2)/_
+ (a^(5/3)*(b*c-a*d)^2)-1/6*d^(5/3)*log(c^(2/3)-c^(1/3)*d^(1/3)*_
+ x+d^(2/3)*x^2)/(c^(2/3)*(b*c-a*d)^2)-1/3*b^(2/3)*(2*b*c-_
+ 5*a*d)*atan((a^(1/3)-2*b^(1/3)*x)/(a^(1/3)*sqrt(3)))/_
+ (a^(5/3)*(b*c-a*d)^2*sqrt(3))-d^(5/3)*atan((c^(1/3)-_
+ 2*d^(1/3)*x)/(c^(1/3)*sqrt(3)))/(c^(2/3)*(b*c-a*d)^2*sqrt(3))
+--R
+--R
+--R (2)
+--R 3 2 +-+3+-+2 3+-+2 2 3+-+2 3+-+3+-+ 3+-+2
+--R (- 3a b d x - 3a d)\|3 \|a \|d log(x \|d - x\|c \|d + \|c )
+--R +
+--R 3 2 +-+3+-+2 3+-+2 3+-+ 3+-+
+--R (6a b d x + 6a d)\|3 \|a \|d log(x\|d + \|c )
+--R +
+--R 2 3 2 +-+3+-+2 3+-+2
+--R ((5a b d - 2b c)x + 5a d - 2a b c)\|3 \|b \|c
+--R *
+--R 2 3+-+2 3+-+3+-+ 3+-+2
+--R log(x \|b - x\|a \|b + \|a )
+--R +
+--R 2 3 2 +-+3+-+2 3+-+2 3+-+ 3+-+
+--R ((- 10a b d + 4b c)x - 10a d + 4a b c)\|3 \|b \|c log(x\|b + \|a )
+--R +
+--R 3+-+ 3+-+
+--R 3 2 3+-+2 3+-+2 2x\|d - \|c
+--R (18a b d x + 18a d)\|a \|d atan(-------------)
+--R +-+3+-+
+--R \|3 \|c
+--R +
+--R 3+-+ 3+-+
+--R 2 3 2 3+-+2 3+-+2 2x\|b - \|a
+--R ((- 30a b d + 12b c)x - 30a d + 12a b c)\|b \|c atan(-------------)
+--R +-+3+-+
+--R \|3 \|a
+--R +
+--R 2 +-+3+-+2 3+-+2
+--R (- 6a b d + 6b c)x\|3 \|a \|c
+--R /
+--R 3 2 2 2 3 2 3 4 2 3 2 2 2 +-+
+--R ((18a b d - 36a b c d + 18a b c )x + 18a d - 36a b c d + 18a b c )\|3
+--R *
+--R 3+-+2 3+-+2
+--R \|a \|c
+--R Type: Expression(Integer)
+--E 949
+
+--S 950 of 994
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +--+ +--+2 +--+
+--R | 2 | 2 | 2
+--R 3 2 +-+ |d 2 |d |d 2 2
+--R (- 3a b d x - 3a d)\|3 |-- log(c |-- - c d x |-- + d x )
+--R 3| 2 3| 2 3| 2
+--R \|c \|c \|c
+--R +
+--R +--+ +--+
+--R | 2 | 2
+--R 3 2 +-+ |d |d
+--R (6a b d x + 6a d)\|3 |-- log(c |-- + d x)
+--R 3| 2 3| 2
+--R \|c \|c
+--R +
+--R +----+
+--R | 2
+--R 2 3 2 +-+ | b
+--R ((- 5a b d + 2b c)x - 5a d + 2a b c)\|3 |- --
+--R 3| 2
+--R \| a
+--R *
+--R +----+2 +----+
+--R | 2 | 2
+--R 2 | b | b 2 2
+--R log(a |- -- + a b x |- -- + b x )
+--R 3| 2 3| 2
+--R \| a \| a
+--R +
+--R +----+ +----+
+--R | 2 | 2
+--R 2 3 2 +-+ | b | b
+--R ((10a b d - 4b c)x + 10a d - 4a b c)\|3 |- -- log(- a |- -- + b x)
+--R 3| 2 3| 2
+--R \| a \| a
+--R +
+--R +----+
+--R | 2
+--R 2 3 2 | b
+--R ((- 30a b d + 12b c)x - 30a d + 12a b c) |- --
+--R 3| 2
+--R \| a
+--R *
+--R +----+
+--R | 2
+--R +-+ | b +-+
+--R a\|3 |- -- + 2b x\|3
+--R 3| 2
+--R \| a
+--R atan(-----------------------)
+--R +----+
+--R | 2
+--R | b
+--R 3a |- --
+--R 3| 2
+--R \| a
+--R +
+--R +--+
+--R | 2
+--R +-+ |d +-+
+--R +--+ c\|3 |-- - 2d x\|3
+--R | 2 3| 2
+--R 3 2 |d \|c
+--R (- 18a b d x - 18a d) |-- atan(---------------------)
+--R 3| 2 +--+
+--R \|c | 2
+--R |d
+--R 3c |--
+--R 3| 2
+--R \|c
+--R +
+--R 2 +-+
+--R (- 6a b d + 6b c)x\|3
+--R /
+--R 3 2 2 2 3 2 3 4 2 3 2 2 2 +-+
+--R ((18a b d - 36a b c d + 18a b c )x + 18a d - 36a b c d + 18a b c )\|3
+--R Type: Union(Expression(Integer),...)
+--E 950
+
+--S 951 of 994
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +--+ +--+2 +--+
+--R | 2 | 2 | 2
+--R +-+3+-+2 3+-+2 |d 2 |d |d 2 2
+--R - 3a d\|3 \|a \|c |-- log(c |-- - c d x |-- + d x )
+--R 3| 2 3| 2 3| 2
+--R \|c \|c \|c
+--R +
+--R +--+ +--+
+--R | 2 | 2
+--R +-+3+-+2 3+-+2 |d |d
+--R 6a d\|3 \|a \|c |-- log(c |-- + d x)
+--R 3| 2 3| 2
+--R \|c \|c
+--R +
+--R +-+3+-+2 3+-+2 2 3+-+2 3+-+3+-+ 3+-+2
+--R 3a d\|3 \|a \|d log(x \|d - x\|c \|d + \|c )
+--R +
+--R +-+3+-+2 3+-+2 3+-+ 3+-+
+--R - 6a d\|3 \|a \|d log(x\|d + \|c )
+--R +
+--R +-+3+-+2 3+-+2 2 3+-+2 3+-+3+-+ 3+-+2
+--R (- 5a d + 2b c)\|3 \|b \|c log(x \|b - x\|a \|b + \|a )
+--R +
+--R +-+3+-+2 3+-+2 3+-+ 3+-+
+--R (10a d - 4b c)\|3 \|b \|c log(x\|b + \|a )
+--R +
+--R +----+ +----+2 +----+
+--R | 2 | 2 | 2
+--R +-+ | b 3+-+2 3+-+2 2 | b | b 2 2
+--R (- 5a d + 2b c)\|3 |- -- \|a \|c log(a |- -- + a b x |- -- + b x )
+--R 3| 2 3| 2 3| 2
+--R \| a \| a \| a
+--R +
+--R +----+ +----+
+--R | 2 | 2
+--R +-+ | b 3+-+2 3+-+2 | b
+--R (10a d - 4b c)\|3 |- -- \|a \|c log(- a |- -- + b x)
+--R 3| 2 3| 2
+--R \| a \| a
+--R +
+--R 3+-+ 3+-+
+--R 3+-+2 3+-+2 2x\|d - \|c
+--R - 18a d \|a \|d atan(-------------)
+--R +-+3+-+
+--R \|3 \|c
+--R +
+--R 3+-+ 3+-+
+--R 3+-+2 3+-+2 2x\|b - \|a
+--R (30a d - 12b c)\|b \|c atan(-------------)
+--R +-+3+-+
+--R \|3 \|a
+--R +
+--R +----+
+--R | 2
+--R +-+ | b +-+
+--R +----+ a\|3 |- -- + 2b x\|3
+--R | 2 3| 2
+--R | b 3+-+2 3+-+2 \| a
+--R (- 30a d + 12b c) |- -- \|a \|c atan(-----------------------)
+--R 3| 2 +----+
+--R \| a | 2
+--R | b
+--R 3a |- --
+--R 3| 2
+--R \| a
+--R +
+--R +--+
+--R | 2
+--R +-+ |d +-+
+--R +--+ c\|3 |-- - 2d x\|3
+--R | 2 3| 2
+--R 3+-+2 3+-+2 |d \|c
+--R - 18a d \|a \|c |-- atan(---------------------)
+--R 3| 2 +--+
+--R \|c | 2
+--R |d
+--R 3c |--
+--R 3| 2
+--R \|c
+--R /
+--R 3 2 2 2 2 +-+3+-+2 3+-+2
+--R (18a d - 36a b c d + 18a b c )\|3 \|a \|c
+--R Type: Expression(Integer)
+--E 951
+
+--S 952 of 994
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 952
+
+)clear all
+
+--S 953 of 994
+t0:=1/((a+b*x^3)^2*(c+d*x^3)^2)
+--R
+--R
+--R (1)
+--R 1
+--R /
+--R 2 2 12 2 2 9 2 2 2 2 6
+--R b d x + (2a b d + 2b c d)x + (a d + 4a b c d + b c )x
+--R +
+--R 2 2 3 2 2
+--R (2a c d + 2a b c )x + a c
+--R Type: Fraction(Polynomial(Integer))
+--E 953
+
+--S 954 of 994
+r0:=1/3*d*(b*c+a*d)*x/(a*c*(b*c-a*d)^2*(c+d*x^3))+1/3*b*x/_
+ (a*(b*c-a*d)*(a+b*x^3)*(c+d*x^3))+2/9*b^(5/3)*(b*c-4*a*d)*_
+ log(a^(1/3)+b^(1/3)*x)/(a^(5/3)*(b*c-a*d)^3)+2/9*d^(5/3)*_
+ (4*b*c-a*d)*log(c^(1/3)+d^(1/3)*x)/(c^(5/3)*(b*c-a*d)^3)-_
+ 1/9*b^(5/3)*(b*c-4*a*d)*log(a^(2/3)-a^(1/3)*b^(1/3)*x+_
+ b^(2/3)*x^2)/(a^(5/3)*(b*c-a*d)^3)-1/9*d^(5/3)*(4*b*c-a*d)*_
+ log(c^(2/3)-c^(1/3)*d^(1/3)*x+d^(2/3)*x^2)/(c^(5/3)*(b*c-_
+ a*d)^3)-2/3*b^(5/3)*(b*c-4*a*d)*atan((a^(1/3)-2*b^(1/3)*x)/_
+ (a^(1/3)*sqrt(3)))/(a^(5/3)*(b*c-a*d)^3*sqrt(3))-_
+ 2/3*d^(5/3)*(4*b*c-a*d)*atan((c^(1/3)-2*d^(1/3)*x)/_
+ (c^(1/3)*sqrt(3)))/(c^(5/3)*(b*c-a*d)^3*sqrt(3))
+--R
+--R
+--R (2)
+--R 2 3 2 2 6 3 3 2 2 2 2 3 3 2
+--R (- a b d + 4a b c d )x + (- a d + 3a b c d + 4a b c d)x - a c d
+--R +
+--R 2 2
+--R 4a b c d
+--R *
+--R +-+3+-+2 3+-+2 2 3+-+2 3+-+3+-+ 3+-+2
+--R \|3 \|a \|d log(x \|d - x\|c \|d + \|c )
+--R +
+--R 2 3 2 2 6 3 3 2 2 2 2 3 3 2
+--R (2a b d - 8a b c d )x + (2a d - 6a b c d - 8a b c d)x + 2a c d
+--R +
+--R 2 2
+--R - 8a b c d
+--R *
+--R +-+3+-+2 3+-+2 3+-+ 3+-+
+--R \|3 \|a \|d log(x\|d + \|c )
+--R +
+--R 2 2 3 2 6 2 2 2 2 3 3 3
+--R (- 4a b c d + b c d)x + (- 4a b c d - 3a b c d + b c )x
+--R +
+--R 2 2 2 3
+--R - 4a b c d + a b c
+--R *
+--R +-+3+-+2 3+-+2 2 3+-+2 3+-+3+-+ 3+-+2
+--R \|3 \|b \|c log(x \|b - x\|a \|b + \|a )
+--R +
+--R 2 2 3 2 6 2 2 2 2 3 3 3 2 2
+--R (8a b c d - 2b c d)x + (8a b c d + 6a b c d - 2b c )x + 8a b c d
+--R +
+--R 2 3
+--R - 2a b c
+--R *
+--R +-+3+-+2 3+-+2 3+-+ 3+-+
+--R \|3 \|b \|c log(x\|b + \|a )
+--R +
+--R 2 3 2 2 6 3 3 2 2 2 2 3
+--R (6a b d - 24a b c d )x + (6a d - 18a b c d - 24a b c d)x
+--R +
+--R 3 2 2 2
+--R 6a c d - 24a b c d
+--R *
+--R 3+-+ 3+-+
+--R 3+-+2 3+-+2 2x\|d - \|c
+--R \|a \|d atan(-------------)
+--R +-+3+-+
+--R \|3 \|c
+--R +
+--R 2 2 3 2 6 2 2 2 2 3 3 3
+--R (24a b c d - 6b c d)x + (24a b c d + 18a b c d - 6b c )x
+--R +
+--R 2 2 2 3
+--R 24a b c d - 6a b c
+--R *
+--R 3+-+ 3+-+
+--R 3+-+2 3+-+2 2x\|b - \|a
+--R \|b \|c atan(-------------)
+--R +-+3+-+
+--R \|3 \|a
+--R +
+--R 2 3 3 2 4 3 3 2 2 2 2 3 3 +-+
+--R ((3a b d - 3b c d)x + (3a d - 3a b c d + 3a b c d - 3b c )x)\|3
+--R *
+--R 3+-+2 3+-+2
+--R \|a \|c
+--R /
+--R 4 4 3 2 2 3 2 3 3 2 4 4 6
+--R (9a b c d - 27a b c d + 27a b c d - 9a b c d)x
+--R +
+--R 5 4 4 2 3 2 3 4 4 5 3 5 2 3 4 3 2
+--R (9a c d - 18a b c d + 18a b c d - 9a b c )x + 9a c d - 27a b c d
+--R +
+--R 3 2 4 2 3 5
+--R 27a b c d - 9a b c
+--R *
+--R +-+3+-+2 3+-+2
+--R \|3 \|a \|c
+--R Type: Expression(Integer)
+--E 954
+
+--S 955 of 994
+--a0:=integrate(t0,x)
+--E 955
+
+--S 956 of 994
+--m0:=a0-r0
+--E 956
+
+--S 957 of 994
+--d0:=D(m0,x)
+--E 957
+
+)clear all
+
+--S 958 of 994
+t0:=(a+b/x^2)/(c+d/x^2)
+--R
+--R
+--R 2
+--R a x + b
+--R (1) --------
+--R 2
+--R c x + d
+--R Type: Fraction(Polynomial(Integer))
+--E 958
+
+--S 959 of 994
+r0:=a*x/c+(b*c-a*d)*atan(x*sqrt(c)/sqrt(d))/(c^(3/2)*sqrt(d))
+--R
+--R
+--R +-+
+--R x\|c +-+ +-+
+--R (- a d + b c)atan(-----) + a x\|c \|d
+--R +-+
+--R \|d
+--R (2) --------------------------------------
+--R +-+ +-+
+--R c\|c \|d
+--R Type: Expression(Integer)
+--E 959
+
+--S 960 of 994
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 2 +-----+
+--R (c x - d)\|- c d - 2c d x +-----+
+--R (a d - b c)log(---------------------------) + 2a x\|- c d
+--R 2
+--R c x + d
+--R [----------------------------------------------------------,
+--R +-----+
+--R 2c\|- c d
+--R +---+
+--R x\|c d +---+
+--R (- a d + b c)atan(-------) + a x\|c d
+--R d
+--R --------------------------------------]
+--R +---+
+--R c\|c d
+--R Type: Union(List(Expression(Integer)),...)
+--E 960
+
+--S 961 of 994
+m0a:=a0.1-r0
+--R
+--R
+--R (4)
+--R 2 +-----+
+--R +-+ +-+ (c x - d)\|- c d - 2c d x
+--R (a d - b c)\|c \|d log(---------------------------)
+--R 2
+--R c x + d
+--R +
+--R +-+
+--R +-----+ x\|c
+--R (2a d - 2b c)\|- c d atan(-----)
+--R +-+
+--R \|d
+--R /
+--R +-----+ +-+ +-+
+--R 2c\|- c d \|c \|d
+--R Type: Expression(Integer)
+--E 961
+
+--S 962 of 994
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 962
+
+--S 963 of 994
+m0b:=a0.2-r0
+--R
+--R
+--R +---+ +-+
+--R +-+ +-+ x\|c d +---+ x\|c
+--R (- a d + b c)\|c \|d atan(-------) + (a d - b c)\|c d atan(-----)
+--R d +-+
+--R \|d
+--R (6) -----------------------------------------------------------------
+--R +-+ +-+ +---+
+--R c\|c \|d \|c d
+--R Type: Expression(Integer)
+--E 963
+
+--S 964 of 994
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 964
+
+)clear all
+
+--S 965 of 994
+t0:=(a+b/x^3)/(c+d/x^3)
+--R
+--R
+--R 3
+--R a x + b
+--R (1) --------
+--R 3
+--R c x + d
+--R Type: Fraction(Polynomial(Integer))
+--E 965
+
+--S 966 of 994
+r0:=a*x/c+1/3*(b*c-a*d)*log(d^(1/3)+c^(1/3)*x)/(c^(4/3)*d^(2/3))-_
+ 1/6*(b*c-a*d)*log(d^(2/3)-c^(1/3)*d^(1/3)*x+c^(2/3)*x^2)/_
+ (c^(4/3)*d^(2/3))-(b*c-a*d)*atan((d^(1/3)-2*c^(1/3)*x)/_
+ (d^(1/3)*sqrt(3)))/(c^(4/3)*d^(2/3)*sqrt(3))
+--R
+--R
+--R (2)
+--R +-+ 3+-+2 3+-+3+-+ 2 3+-+2
+--R (a d - b c)\|3 log(\|d - x\|c \|d + x \|c )
+--R +
+--R 3+-+ 3+-+
+--R +-+ 3+-+ 3+-+ \|d - 2x\|c
+--R (- 2a d + 2b c)\|3 log(\|d + x\|c ) + (6a d - 6b c)atan(-------------)
+--R +-+3+-+
+--R \|3 \|d
+--R +
+--R +-+3+-+3+-+2
+--R 6a x\|3 \|c \|d
+--R /
+--R +-+3+-+3+-+2
+--R 6c\|3 \|c \|d
+--R Type: Expression(Integer)
+--E 966
+
+--S 967 of 994
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +------+2 +------+
+--R +-+ 2 3| 2 3| 2 2
+--R (- a d + b c)\|3 log(x \|- c d + d x\|- c d + d )
+--R +
+--R +------+
+--R +-+ 3| 2
+--R (2a d - 2b c)\|3 log(x\|- c d - d)
+--R +
+--R +------+
+--R +-+3| 2 +-+ +------+
+--R 2x\|3 \|- c d + d\|3 +-+3| 2
+--R (- 6a d + 6b c)atan(-----------------------) + 6a x\|3 \|- c d
+--R 3d
+--R /
+--R +------+
+--R +-+3| 2
+--R 6c\|3 \|- c d
+--R Type: Union(Expression(Integer),...)
+--E 967
+
+--S 968 of 994
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R +------+
+--R +-+3| 2 3+-+2 3+-+3+-+ 2 3+-+2
+--R (- a d + b c)\|3 \|- c d log(\|d - x\|c \|d + x \|c )
+--R +
+--R +------+
+--R +-+3| 2 3+-+ 3+-+
+--R (2a d - 2b c)\|3 \|- c d log(\|d + x\|c )
+--R +
+--R +------+2 +------+
+--R +-+3+-+3+-+2 2 3| 2 3| 2 2
+--R (- a d + b c)\|3 \|c \|d log(x \|- c d + d x\|- c d + d )
+--R +
+--R +------+
+--R +-+3+-+3+-+2 3| 2
+--R (2a d - 2b c)\|3 \|c \|d log(x\|- c d - d)
+--R +
+--R +------+
+--R +-+3| 2 +-+
+--R 3+-+3+-+2 2x\|3 \|- c d + d\|3
+--R (- 6a d + 6b c)\|c \|d atan(-----------------------)
+--R 3d
+--R +
+--R +------+ 3+-+ 3+-+
+--R 3| 2 \|d - 2x\|c
+--R (- 6a d + 6b c)\|- c d atan(-------------)
+--R +-+3+-+
+--R \|3 \|d
+--R /
+--R +------+
+--R +-+3| 2 3+-+3+-+2
+--R 6c\|3 \|- c d \|c \|d
+--R Type: Expression(Integer)
+--E 968
+
+--S 969 of 994
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 969
+
+)clear all
+
+--S 970 of 994
+t0:=(a+b*sqrt(x))/(c+d*sqrt(x))
+--R
+--R
+--R +-+
+--R b\|x + a
+--R (1) ---------
+--R +-+
+--R d\|x + c
+--R Type: Expression(Integer)
+--E 970
+
+--S 971 of 994
+r0:=b*x/d+2*c*(b*c-a*d)*log(c+d*sqrt(x))/d^3-2*(b*c-a*d)*sqrt(x)/d^2
+--R
+--R
+--R 2 +-+ 2 +-+ 2
+--R (- 2a c d + 2b c )log(d\|x + c) + (2a d - 2b c d)\|x + b d x
+--R (2) ---------------------------------------------------------------
+--R 3
+--R d
+--R Type: Expression(Integer)
+--E 971
+
+--S 972 of 994
+a0:=integrate(t0,x)
+--R
+--R
+--R 2 +-+ 2 +-+ 2
+--R (- 2a c d + 2b c )log(d\|x + c) + (2a d - 2b c d)\|x + b d x
+--R (3) ---------------------------------------------------------------
+--R 3
+--R d
+--R Type: Union(Expression(Integer),...)
+--E 972
+
+--S 973 of 994
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 973
+
+--S 974 of 994
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 974
+
+)clear all
+
+--S 975 of 994
+t0:=(-1+x^(1/3))/(1+x^(1/3))
+--R
+--R
+--R 3+-+
+--R \|x - 1
+--R (1) --------
+--R 3+-+
+--R \|x + 1
+--R Type: Expression(Integer)
+--E 975
+
+--S 976 of 994
+r0:=6*x^(1/3)-3*x^(2/3)+x-6*log(1+x^(1/3))
+--R
+--R
+--R 3+-+ 3+-+2 3+-+
+--R (2) - 6log(\|x + 1) - 3\|x + 6\|x + x
+--R Type: Expression(Integer)
+--E 976
+
+--S 977 of 994
+a0:=integrate(t0,x)
+--R
+--R
+--R 3+-+ 3+-+2 3+-+
+--R (3) - 6log(\|x + 1) - 3\|x + 6\|x + x
+--R Type: Union(Expression(Integer),...)
+--E 977
+
+--S 978 of 994
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 978
+
+--S 979 of 994
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 979
+
+)clear all
+
+--S 980 of 994
+t0:=(1+1/x^(1/3))/(-1+1/x^(1/3))
+--R
+--R
+--R 3+-+
+--R - \|x - 1
+--R (1) ----------
+--R 3+-+
+--R \|x - 1
+--R Type: Expression(Integer)
+--E 980
+
+--S 981 of 994
+r0:=-6*x^(1/3)-3*x^(2/3)-x-6*log(1-x^(1/3))
+--R
+--R
+--R 3+-+ 3+-+2 3+-+
+--R (2) - 6log(- \|x + 1) - 3\|x - 6\|x - x
+--R Type: Expression(Integer)
+--E 981
+
+--S 982 of 994
+a0:=integrate(t0,x)
+--R
+--R
+--R 3+-+ 3+-+2 3+-+
+--R (3) - 6log(\|x - 1) - 3\|x - 6\|x - x
+--R Type: Union(Expression(Integer),...)
+--E 982
+
+--S 983 of 994
+m0:=a0-r0
+--R
+--R
+--R 3+-+ 3+-+
+--R (4) - 6log(\|x - 1) + 6log(- \|x + 1)
+--R Type: Expression(Integer)
+--E 983
+
+--S 984 of 994
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 984
+
+)clear all
+
+--S 985 of 994
+t0:=(1+x^(2/3))/(-1+x^(2/3))
+--R
+--R
+--R 3+-+2
+--R \|x + 1
+--R (1) ---------
+--R 3+-+2
+--R \|x - 1
+--R Type: Expression(Integer)
+--E 985
+
+--S 986 of 994
+r0:=6*x^(1/3)+x-6*atanh(x^(1/3))
+--R
+--R
+--R 3+-+ 3+-+
+--R (2) - 6atanh(\|x ) + 6\|x + x
+--R Type: Expression(Integer)
+--E 986
+
+--S 987 of 994
+a0:=integrate(t0,x)
+--R
+--R
+--R 3+-+ 3+-+ 3+-+
+--R (3) - 3log(\|x + 1) + 3log(\|x - 1) + 6\|x + x
+--R Type: Union(Expression(Integer),...)
+--E 987
+
+--S 988 of 994
+m0:=a0-r0
+--R
+--R
+--R 3+-+ 3+-+ 3+-+
+--R (4) - 3log(\|x + 1) + 3log(\|x - 1) + 6atanh(\|x )
+--R Type: Expression(Integer)
+--E 988
+
+--S 989 of 994
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 989
+
+)clear all
+
+--S 990 of 994
+t0:=(-16+x^(3/4))/(16+x^(3/4))
+--R
+--R
+--R 4+-+3
+--R \|x - 16
+--R (1) ----------
+--R 4+-+3
+--R \|x + 16
+--R Type: Expression(Integer)
+--E 990
+
+--S 991 of 994
+r0:=-128*x^(1/4)+x+256/3*2^(1/3)*log(2*2^(1/3)+x^(1/4))-128/3*2^(1/3)*_
+ log(4*2^(2/3)-2*2^(1/3)*x^(1/4)+sqrt(x))-256*2^(1/3)*_
+ atan((2^(1/3)-x^(1/4))/(2^(1/3)*sqrt(3)))/sqrt(3)
+--R
+--R
+--R (2)
+--R 3+-+ +-+ 4+-+ 3+-+
+--R 256\|2 \|3 log(\|x + 2\|2 )
+--R +
+--R 4+-+ 3+-+
+--R 3+-+ +-+ 3+-+4+-+ +-+ 3+-+2 3+-+ \|x - \|2
+--R - 128\|2 \|3 log(- 2\|2 \|x + \|x + 4\|2 ) + 768\|2 atan(-----------)
+--R 3+-+ +-+
+--R \|2 \|3
+--R +
+--R +-+4+-+ +-+
+--R - 384\|3 \|x + 3x\|3
+--R /
+--R +-+
+--R 3\|3
+--R Type: Expression(Integer)
+--E 991
+
+--S 992 of 994
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 3+-+ +-+ 4+-+2 3+-+4+-+ 3+-+2
+--R - 128\|2 \|3 log(\|x - 2\|2 \|x + 4\|2 )
+--R +
+--R +-+4+-+ 3+-+ +-+
+--R 3+-+ +-+ 4+-+ 3+-+ 3+-+ \|3 \|x - \|2 \|3
+--R 256\|2 \|3 log(\|x + 2\|2 ) + 768\|2 atan(-------------------)
+--R 3+-+
+--R 3\|2
+--R +
+--R +-+4+-+ +-+
+--R - 384\|3 \|x + 3x\|3
+--R /
+--R +-+
+--R 3\|3
+--R Type: Union(Expression(Integer),...)
+--E 992
+
+--S 993 of 994
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R 3+-+ +-+ 4+-+2 3+-+4+-+ 3+-+2
+--R - 128\|2 \|3 log(\|x - 2\|2 \|x + 4\|2 )
+--R +
+--R 3+-+ +-+ 3+-+4+-+ +-+ 3+-+2
+--R 128\|2 \|3 log(- 2\|2 \|x + \|x + 4\|2 )
+--R +
+--R +-+4+-+ 3+-+ +-+ 4+-+ 3+-+
+--R 3+-+ \|3 \|x - \|2 \|3 3+-+ \|x - \|2
+--R 768\|2 atan(-------------------) - 768\|2 atan(-----------)
+--R 3+-+ 3+-+ +-+
+--R 3\|2 \|2 \|3
+--R /
+--R +-+
+--R 3\|3
+--R Type: Expression(Integer)
+--E 993
+
+--S 994 of 994
+d0:=D(m0,x)
+--R
+--R
+--R (5)
+--R 3+-+2 +-+ 3+-+ 4+-+3
+--R ((- 64x \|2 - 20480)\|x + 3584x\|2 )\|x
+--R +
+--R 3+-+ +-+ 3+-+2 4+-+2
+--R ((16384\|2 + 1024x)\|x - 8192x \|2 )\|x
+--R +
+--R 3+-+ +-+ 2 3+-+2 4+-+ 3+-+2 +-+ 3+-+
+--R (- 3584x\|2 \|x + 64x \|2 + 20480x)\|x + 8192x \|2 \|x - 16384x\|2
+--R +
+--R 2
+--R - 1024x
+--R /
+--R 3+-+2 2 3+-+ +-+ 2 4+-+3
+--R ((2496x \|2 + 6x \|2)\|x + 336x )\|x
+--R +
+--R 2 3+-+2 +-+ 2 3+-+ 3 4+-+2
+--R ((- 48x \|2 - 6912x)\|x - 576x \|2 - 3x )\|x
+--R +
+--R 3+-+ 2 +-+ 2 3+-+2 3 3+-+4+-+
+--R ((6144x\|2 + 432x )\|x + 576x \|2 + 18x \|2)\|x
+--R +
+--R 3+-+2 2 3+-+ +-+ 3 3+-+2 2
+--R (- 3072x \|2 - 1248x \|2)\|x - 72x \|2 - 768x
+--R Type: Expression(Integer)
+--E 994
+
+)spool
+)lisp (bye)
+
+\end{chunk}
+\eject
+\begin{thebibliography}{99}
+\bibitem{1} nothing
+\end{thebibliography}
+\end{document}
diff --git a/src/axiom-website/CATS/rich5.input.pdf b/src/axiom-website/CATS/rich5.input.pdf
new file mode 100644
index 0000000..2457659
Binary files /dev/null and b/src/axiom-website/CATS/rich5.input.pdf differ
diff --git a/src/axiom-website/CATS/rich6a.input.pamphlet b/src/axiom-website/CATS/rich6a.input.pamphlet
new file mode 100644
index 0000000..6da82f5
--- /dev/null
+++ b/src/axiom-website/CATS/rich6a.input.pamphlet
@@ -0,0 +1,28754 @@
+\documentclass{article}
+\usepackage{axiom}
+\setlength{\textwidth}{400pt}
+\begin{document}
+\title{\$SPAD/src/input rich6a.input}
+\author{Albert Rich and Timothy Daly}
+\maketitle
+\begin{abstract}
+\verb|x^m (a+b x^n)^p (c+d x^n)^q|
+There are:
+\begin{itemize}
+\item 255 integrals in this file.
+\item 260 supplied "optimal results".
+\item 318 matching answers.
+\item 58 cases where Axiom supplied 2 results.
+\item 0 cases that Axiom failed to integrate.
+\item 0 that contain expressions Axiom does not recognize.
+\end{itemize}
+\end{abstract}
+\eject
+\tableofcontents
+\eject
+\begin{chunk}{*}
+)set break resume
+)sys rm -f rich6a.output
+)spool rich6a.output
+)set message test on
+)set message auto off
+)clear all
+
+--S 1 of 1406
+t0:=x^m*(a+b*x^2)*(A+B*x^2)
+--R
+--R
+--R 4 2 m
+--R (1) (B b x + (A b + B a)x + A a)x
+--R Type: Expression(Integer)
+--E 1
+
+--S 2 of 1406
+r0:=a*A*x^(1+m)/(1+m)+(A*b+a*B)*x^(3+m)/(3+m)+b*B*x^(5+m)/(5+m)
+--R
+--R
+--R (2)
+--R 2 m + 5
+--R (B b m + 4B b m + 3B b)x
+--R +
+--R 2 m + 3
+--R ((A b + B a)m + (6A b + 6B a)m + 5A b + 5B a)x
+--R +
+--R 2 m + 1
+--R (A a m + 8A a m + 15A a)x
+--R /
+--R 3 2
+--R m + 9m + 23m + 15
+--R Type: Expression(Integer)
+--E 2
+
+--S 3 of 1406
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 2 5
+--R (B b m + 4B b m + 3B b)x
+--R +
+--R 2 3
+--R ((A b + B a)m + (6A b + 6B a)m + 5A b + 5B a)x
+--R +
+--R 2
+--R (A a m + 8A a m + 15A a)x
+--R *
+--R m log(x)
+--R %e
+--R /
+--R 3 2
+--R m + 9m + 23m + 15
+--R Type: Union(Expression(Integer),...)
+--E 3
+
+--S 4 of 1406
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R 2 5
+--R (B b m + 4B b m + 3B b)x
+--R +
+--R 2 3
+--R ((A b + B a)m + (6A b + 6B a)m + 5A b + 5B a)x
+--R +
+--R 2
+--R (A a m + 8A a m + 15A a)x
+--R *
+--R m log(x)
+--R %e
+--R +
+--R 2 m + 5
+--R (- B b m - 4B b m - 3B b)x
+--R +
+--R 2 m + 3
+--R ((- A b - B a)m + (- 6A b - 6B a)m - 5A b - 5B a)x
+--R +
+--R 2 m + 1
+--R (- A a m - 8A a m - 15A a)x
+--R /
+--R 3 2
+--R m + 9m + 23m + 15
+--R Type: Expression(Integer)
+--E 4
+
+--S 5 of 1406
+d0:=normalize m0
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 5
+
+)clear all
+
+--S 6 of 1406
+t0:=x^2*(a+b*x^2)*(A+B*x^2)
+--R
+--R
+--R 6 4 2
+--R (1) B b x + (A b + B a)x + A a x
+--R Type: Polynomial(Integer)
+--E 6
+
+--S 7 of 1406
+r0:=1/3*a*A*x^3+1/5*(A*b+a*B)*x^5+1/7*b*B*x^7
+--R
+--R
+--R 1 7 1 1 5 1 3
+--R (2) - B b x + (- A b + - B a)x + - A a x
+--R 7 5 5 3
+--R Type: Polynomial(Fraction(Integer))
+--E 7
+
+--S 8 of 1406
+a0:=integrate(t0,x)
+--R
+--R
+--R 1 7 1 1 5 1 3
+--R (3) - B b x + (- A b + - B a)x + - A a x
+--R 7 5 5 3
+--R Type: Polynomial(Fraction(Integer))
+--E 8
+
+--S 9 of 1406
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Polynomial(Fraction(Integer))
+--E 9
+
+--S 10 of 1406
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Polynomial(Fraction(Integer))
+--E 10
+
+)clear all
+
+--S 11 of 1406
+t0:=x*(a+b*x^2)*(A+B*x^2)
+--R
+--R
+--R 5 3
+--R (1) B b x + (A b + B a)x + A a x
+--R Type: Polynomial(Integer)
+--E 11
+
+--S 12 of 1406
+r0:=1/2*a*A*x^2+1/4*(A*b+a*B)*x^4+1/6*b*B*x^6
+--R
+--R
+--R 1 6 1 1 4 1 2
+--R (2) - B b x + (- A b + - B a)x + - A a x
+--R 6 4 4 2
+--R Type: Polynomial(Fraction(Integer))
+--E 12
+
+--S 13 of 1406
+a0:=integrate(t0,x)
+--R
+--R
+--R 1 6 1 1 4 1 2
+--R (3) - B b x + (- A b + - B a)x + - A a x
+--R 6 4 4 2
+--R Type: Polynomial(Fraction(Integer))
+--E 13
+
+--S 14 of 1406
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Polynomial(Fraction(Integer))
+--E 14
+
+--S 15 of 1406
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Polynomial(Fraction(Integer))
+--E 15
+
+)clear all
+
+--S 16 of 1406
+t0:=(a+b*x^2)*(A+B*x^2)
+--R
+--R
+--R 4 2
+--R (1) B b x + (A b + B a)x + A a
+--R Type: Polynomial(Integer)
+--E 16
+
+--S 17 of 1406
+r0:=a*A*x+1/3*(A*b+a*B)*x^3+1/5*b*B*x^5
+--R
+--R
+--R 1 5 1 1 3
+--R (2) - B b x + (- A b + - B a)x + A a x
+--R 5 3 3
+--R Type: Polynomial(Fraction(Integer))
+--E 17
+
+--S 18 of 1406
+a0:=integrate(t0,x)
+--R
+--R
+--R 1 5 1 1 3
+--R (3) - B b x + (- A b + - B a)x + A a x
+--R 5 3 3
+--R Type: Polynomial(Fraction(Integer))
+--E 18
+
+--S 19 of 1406
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Polynomial(Fraction(Integer))
+--E 19
+
+--S 20 of 1406
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Polynomial(Fraction(Integer))
+--E 20
+
+)clear all
+
+--S 21 of 1406
+t0:=(a+b*x^2)*(A+B*x^2)/x
+--R
+--R
+--R 4 2
+--R B b x + (A b + B a)x + A a
+--R (1) ----------------------------
+--R x
+--R Type: Fraction(Polynomial(Integer))
+--E 21
+
+--S 22 of 1406
+r0:=1/2*(A*b+a*B)*x^2+1/4*b*B*x^4+a*A*log(x)
+--R
+--R
+--R 4 2
+--R 4A a log(x) + B b x + (2A b + 2B a)x
+--R (2) --------------------------------------
+--R 4
+--R Type: Expression(Integer)
+--E 22
+
+--S 23 of 1406
+a0:=integrate(t0,x)
+--R
+--R
+--R 4 2
+--R 4A a log(x) + B b x + (2A b + 2B a)x
+--R (3) --------------------------------------
+--R 4
+--R Type: Union(Expression(Integer),...)
+--E 23
+
+--S 24 of 1406
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 24
+
+--S 25 of 1406
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 25
+
+)clear all
+
+--S 26 of 1406
+t0:=(a+b*x^2)*(A+B*x^2)/x^2
+--R
+--R
+--R 4 2
+--R B b x + (A b + B a)x + A a
+--R (1) ----------------------------
+--R 2
+--R x
+--R Type: Fraction(Polynomial(Integer))
+--E 26
+
+--S 27 of 1406
+r0:=-a*A/x+(A*b+a*B)*x+1/3*b*B*x^3
+--R
+--R
+--R 4 2
+--R B b x + (3A b + 3B a)x - 3A a
+--R (2) -------------------------------
+--R 3x
+--R Type: Fraction(Polynomial(Integer))
+--E 27
+
+--S 28 of 1406
+a0:=integrate(t0,x)
+--R
+--R
+--R 4 2
+--R B b x + (3A b + 3B a)x - 3A a
+--R (3) -------------------------------
+--R 3x
+--R Type: Union(Expression(Integer),...)
+--E 28
+
+--S 29 of 1406
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 29
+
+--S 30 of 1406
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 30
+
+)clear all
+
+--S 31 of 1406
+t0:=(a+b*x^2)*(A+B*x^2)/x^3
+--R
+--R
+--R 4 2
+--R B b x + (A b + B a)x + A a
+--R (1) ----------------------------
+--R 3
+--R x
+--R Type: Fraction(Polynomial(Integer))
+--E 31
+
+--S 32 of 1406
+r0:=-1/2*a*A/x^2+1/2*b*B*x^2+(A*b+a*B)*log(x)
+--R
+--R
+--R 2 4
+--R (2A b + 2B a)x log(x) + B b x - A a
+--R (2) ------------------------------------
+--R 2
+--R 2x
+--R Type: Expression(Integer)
+--E 32
+
+--S 33 of 1406
+a0:=integrate(t0,x)
+--R
+--R
+--R 2 4
+--R (2A b + 2B a)x log(x) + B b x - A a
+--R (3) ------------------------------------
+--R 2
+--R 2x
+--R Type: Union(Expression(Integer),...)
+--E 33
+
+--S 34 of 1406
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 34
+
+--S 35 of 1406
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 35
+
+)clear all
+
+--S 36 of 1406
+t0:=(a+b*x^2)*(A+B*x^2)/x^4
+--R
+--R
+--R 4 2
+--R B b x + (A b + B a)x + A a
+--R (1) ----------------------------
+--R 4
+--R x
+--R Type: Fraction(Polynomial(Integer))
+--E 36
+
+--S 37 of 1406
+r0:=-1/3*a*A/x^3+(-A*b-a*B)/x+b*B*x
+--R
+--R
+--R 4 2 1
+--R B b x + (- A b - B a)x - - A a
+--R 3
+--R (2) --------------------------------
+--R 3
+--R x
+--R Type: Fraction(Polynomial(Fraction(Integer)))
+--E 37
+
+--S 38 of 1406
+a0:=integrate(t0,x)
+--R
+--R
+--R 4 2
+--R 3B b x + (- 3A b - 3B a)x - A a
+--R (3) ---------------------------------
+--R 3
+--R 3x
+--R Type: Union(Expression(Integer),...)
+--E 38
+
+--S 39 of 1406
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 39
+
+--S 40 of 1406
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 40
+
+)clear all
+
+--S 41 of 1406
+t0:=(a+b*x^2)*(A+B*x^2)/x^5
+--R
+--R
+--R 4 2
+--R B b x + (A b + B a)x + A a
+--R (1) ----------------------------
+--R 5
+--R x
+--R Type: Fraction(Polynomial(Integer))
+--E 41
+
+--S 42 of 1406
+r0:=-1/4*a*A/x^4+1/2*(-A*b-a*B)/x^2+b*B*log(x)
+--R
+--R
+--R 4 2
+--R 4B b x log(x) + (- 2A b - 2B a)x - A a
+--R (2) ---------------------------------------
+--R 4
+--R 4x
+--R Type: Expression(Integer)
+--E 42
+
+--S 43 of 1406
+a0:=integrate(t0,x)
+--R
+--R
+--R 4 2
+--R 4B b x log(x) + (- 2A b - 2B a)x - A a
+--R (3) ---------------------------------------
+--R 4
+--R 4x
+--R Type: Union(Expression(Integer),...)
+--E 43
+
+--S 44 of 1406
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 44
+
+--S 45 of 1406
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 45
+
+)clear all
+
+--S 46 of 1406
+t0:=(a+b*x^2)*(A+B*x^2)/x^6
+--R
+--R
+--R 4 2
+--R B b x + (A b + B a)x + A a
+--R (1) ----------------------------
+--R 6
+--R x
+--R Type: Fraction(Polynomial(Integer))
+--E 46
+
+--S 47 of 1406
+r0:=-1/5*a*A/x^5+1/3*(-A*b-a*B)/x^3-b*B/x
+--R
+--R
+--R 4 1 1 2 1
+--R - B b x + (- - A b - - B a)x - - A a
+--R 3 3 5
+--R (2) --------------------------------------
+--R 5
+--R x
+--R Type: Fraction(Polynomial(Fraction(Integer)))
+--E 47
+
+--S 48 of 1406
+a0:=integrate(t0,x)
+--R
+--R
+--R 4 2
+--R - 15B b x + (- 5A b - 5B a)x - 3A a
+--R (3) -------------------------------------
+--R 5
+--R 15x
+--R Type: Union(Expression(Integer),...)
+--E 48
+
+--S 49 of 1406
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 49
+
+--S 50 of 1406
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 50
+
+)clear all
+
+--S 51 of 1406
+t0:=(a+b*x^2)*(A+B*x^2)/x^7
+--R
+--R
+--R 4 2
+--R B b x + (A b + B a)x + A a
+--R (1) ----------------------------
+--R 7
+--R x
+--R Type: Fraction(Polynomial(Integer))
+--E 51
+
+--S 52 of 1406
+r0:=-1/6*a*A/x^6+1/4*(-A*b-a*B)/x^4-1/2*b*B/x^2
+--R
+--R
+--R 1 4 1 1 2 1
+--R - - B b x + (- - A b - - B a)x - - A a
+--R 2 4 4 6
+--R (2) ----------------------------------------
+--R 6
+--R x
+--R Type: Fraction(Polynomial(Fraction(Integer)))
+--E 52
+
+--S 53 of 1406
+a0:=integrate(t0,x)
+--R
+--R
+--R 4 2
+--R - 6B b x + (- 3A b - 3B a)x - 2A a
+--R (3) ------------------------------------
+--R 6
+--R 12x
+--R Type: Union(Expression(Integer),...)
+--E 53
+
+--S 54 of 1406
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 54
+
+--S 55 of 1406
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 55
+
+)clear all
+
+--S 56 of 1406
+t0:=x^m*(a+b*x^2)^2*(A+B*x^2)
+--R
+--R
+--R 2 6 2 4 2 2 2 m
+--R (1) (B b x + (A b + 2B a b)x + (2A a b + B a )x + A a )x
+--R Type: Expression(Integer)
+--E 56
+
+--S 57 of 1406
+r0:=a^2*A*x^(1+m)/(1+m)+a*(2*A*b+a*B)*x^(3+m)/(3+m)+b*(A*b+2*a*B)*_
+ x^(5+m)/(5+m)+b^2*B*x^(7+m)/(7+m)
+--R
+--R
+--R (2)
+--R 2 3 2 2 2 2 m + 7
+--R (B b m + 9B b m + 23B b m + 15B b )x
+--R +
+--R 2 3 2 2 2
+--R (A b + 2B a b)m + (11A b + 22B a b)m + (31A b + 62B a b)m
+--R +
+--R 2
+--R 21A b + 42B a b
+--R *
+--R m + 5
+--R x
+--R +
+--R 2 3 2 2 2
+--R (2A a b + B a )m + (26A a b + 13B a )m + (94A a b + 47B a )m
+--R +
+--R 2
+--R 70A a b + 35B a
+--R *
+--R m + 3
+--R x
+--R +
+--R 2 3 2 2 2 2 m + 1
+--R (A a m + 15A a m + 71A a m + 105A a )x
+--R /
+--R 4 3 2
+--R m + 16m + 86m + 176m + 105
+--R Type: Expression(Integer)
+--E 57
+
+--S 58 of 1406
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 2 3 2 2 2 2 7
+--R (B b m + 9B b m + 23B b m + 15B b )x
+--R +
+--R 2 3 2 2 2
+--R (A b + 2B a b)m + (11A b + 22B a b)m + (31A b + 62B a b)m
+--R +
+--R 2
+--R 21A b + 42B a b
+--R *
+--R 5
+--R x
+--R +
+--R 2 3 2 2 2
+--R (2A a b + B a )m + (26A a b + 13B a )m + (94A a b + 47B a )m
+--R +
+--R 2
+--R 70A a b + 35B a
+--R *
+--R 3
+--R x
+--R +
+--R 2 3 2 2 2 2
+--R (A a m + 15A a m + 71A a m + 105A a )x
+--R *
+--R m log(x)
+--R %e
+--R /
+--R 4 3 2
+--R m + 16m + 86m + 176m + 105
+--R Type: Union(Expression(Integer),...)
+--E 58
+
+--S 59 of 1406
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R 2 3 2 2 2 2 7
+--R (B b m + 9B b m + 23B b m + 15B b )x
+--R +
+--R 2 3 2 2 2
+--R (A b + 2B a b)m + (11A b + 22B a b)m + (31A b + 62B a b)m
+--R +
+--R 2
+--R 21A b + 42B a b
+--R *
+--R 5
+--R x
+--R +
+--R 2 3 2 2 2
+--R (2A a b + B a )m + (26A a b + 13B a )m + (94A a b + 47B a )m
+--R +
+--R 2
+--R 70A a b + 35B a
+--R *
+--R 3
+--R x
+--R +
+--R 2 3 2 2 2 2
+--R (A a m + 15A a m + 71A a m + 105A a )x
+--R *
+--R m log(x)
+--R %e
+--R +
+--R 2 3 2 2 2 2 m + 7
+--R (- B b m - 9B b m - 23B b m - 15B b )x
+--R +
+--R 2 3 2 2 2
+--R (- A b - 2B a b)m + (- 11A b - 22B a b)m + (- 31A b - 62B a b)m
+--R +
+--R 2
+--R - 21A b - 42B a b
+--R *
+--R m + 5
+--R x
+--R +
+--R 2 3 2 2 2
+--R (- 2A a b - B a )m + (- 26A a b - 13B a )m + (- 94A a b - 47B a )m
+--R +
+--R 2
+--R - 70A a b - 35B a
+--R *
+--R m + 3
+--R x
+--R +
+--R 2 3 2 2 2 2 m + 1
+--R (- A a m - 15A a m - 71A a m - 105A a )x
+--R /
+--R 4 3 2
+--R m + 16m + 86m + 176m + 105
+--R Type: Expression(Integer)
+--E 59
+
+--S 60 of 1406
+d0:=normalize(D(m0,x))
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 60
+
+)clear all
+
+--S 61 of 1406
+t0:=x^2*(a+b*x^2)^2*(A+B*x^2)
+--R
+--R
+--R 2 8 2 6 2 4 2 2
+--R (1) B b x + (A b + 2B a b)x + (2A a b + B a )x + A a x
+--R Type: Polynomial(Integer)
+--E 61
+
+--S 62 of 1406
+r0:=1/3*a^2*A*x^3+1/5*a*(2*A*b+a*B)*x^5+1/7*b*(A*b+2*a*B)*x^7+1/9*b^2*B*x^9
+--R
+--R
+--R 1 2 9 1 2 2 7 2 1 2 5 1 2 3
+--R (2) - B b x + (- A b + - B a b)x + (- A a b + - B a )x + - A a x
+--R 9 7 7 5 5 3
+--R Type: Polynomial(Fraction(Integer))
+--E 62
+
+--S 63 of 1406
+a0:=integrate(t0,x)
+--R
+--R
+--R 1 2 9 1 2 2 7 2 1 2 5 1 2 3
+--R (3) - B b x + (- A b + - B a b)x + (- A a b + - B a )x + - A a x
+--R 9 7 7 5 5 3
+--R Type: Polynomial(Fraction(Integer))
+--E 63
+
+--S 64 of 1406
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Polynomial(Fraction(Integer))
+--E 64
+
+--S 65 of 1406
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Polynomial(Fraction(Integer))
+--E 65
+
+)clear all
+
+--S 66 of 1406
+t0:=x*(a+b*x^2)^2*(A+B*x^2)
+--R
+--R
+--R 2 7 2 5 2 3 2
+--R (1) B b x + (A b + 2B a b)x + (2A a b + B a )x + A a x
+--R Type: Polynomial(Integer)
+--E 66
+
+--S 67 of 1406
+r0:=1/6*(A*b-a*B)*(a+b*x^2)^3/b^2+1/8*B*(a+b*x^2)^4/b^2
+--R
+--R
+--R (2)
+--R 1 4 8 1 4 1 3 6 1 3 1 2 2 4 1 2 2 2
+--R - B b x + (- A b + - B a b )x + (- A a b + - B a b )x + - A a b x
+--R 8 6 3 2 4 2
+--R +
+--R 1 3 1 4
+--R - A a b - -- B a
+--R 6 24
+--R /
+--R 2
+--R b
+--R Type: Fraction(Polynomial(Fraction(Integer)))
+--E 67
+
+--S 68 of 1406
+a0:=integrate(t0,x)
+--R
+--R
+--R 1 2 8 1 2 1 6 1 1 2 4 1 2 2
+--R (3) - B b x + (- A b + - B a b)x + (- A a b + - B a )x + - A a x
+--R 8 6 3 2 4 2
+--R Type: Polynomial(Fraction(Integer))
+--E 68
+
+--S 69 of 1406
+m0:=a0-r0
+--R
+--R
+--R 1 3 1 4
+--R - - A a b + -- B a
+--R 6 24
+--R (4) -------------------
+--R 2
+--R b
+--R Type: Fraction(Polynomial(Fraction(Integer)))
+--E 69
+
+--S 70 of 1406
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Fraction(Polynomial(Fraction(Integer)))
+--E 70
+
+)clear all
+
+--S 71 of 1406
+t0:=(a+b*x^2)^2*(A+B*x^2)
+--R
+--R
+--R 2 6 2 4 2 2 2
+--R (1) B b x + (A b + 2B a b)x + (2A a b + B a )x + A a
+--R Type: Polynomial(Integer)
+--E 71
+
+--S 72 of 1406
+r0:=a^2*A*x+1/3*a*(2*A*b+a*B)*x^3+1/5*b*(A*b+2*a*B)*x^5+1/7*b^2*B*x^7
+--R
+--R
+--R 1 2 7 1 2 2 5 2 1 2 3 2
+--R (2) - B b x + (- A b + - B a b)x + (- A a b + - B a )x + A a x
+--R 7 5 5 3 3
+--R Type: Polynomial(Fraction(Integer))
+--E 72
+
+--S 73 of 1406
+a0:=integrate(t0,x)
+--R
+--R
+--R 1 2 7 1 2 2 5 2 1 2 3 2
+--R (3) - B b x + (- A b + - B a b)x + (- A a b + - B a )x + A a x
+--R 7 5 5 3 3
+--R Type: Polynomial(Fraction(Integer))
+--E 73
+
+--S 74 of 1406
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Polynomial(Fraction(Integer))
+--E 74
+
+--S 75 of 1406
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Polynomial(Fraction(Integer))
+--E 75
+
+)clear all
+
+--S 76 of 1406
+t0:=(a+b*x^2)^2*(A+B*x^2)/x
+--R
+--R
+--R 2 6 2 4 2 2 2
+--R B b x + (A b + 2B a b)x + (2A a b + B a )x + A a
+--R (1) -----------------------------------------------------
+--R x
+--R Type: Fraction(Polynomial(Integer))
+--E 76
+
+--S 77 of 1406
+r0:=a*A*b*x^2+1/4*A*b^2*x^4+1/6*B*(a+b*x^2)^3/b+a^2*A*log(x)
+--R
+--R
+--R (2)
+--R 2 3 6 3 2 4 2 2 2
+--R 12A a b log(x) + 2B b x + (3A b + 6B a b )x + (12A a b + 6B a b)x
+--R +
+--R 3
+--R 2B a
+--R /
+--R 12b
+--R Type: Expression(Integer)
+--E 77
+
+--S 78 of 1406
+a0:=integrate(t0,x)
+--R
+--R
+--R 2 2 6 2 4 2 2
+--R 12A a log(x) + 2B b x + (3A b + 6B a b)x + (12A a b + 6B a )x
+--R (3) -----------------------------------------------------------------
+--R 12
+--R Type: Union(Expression(Integer),...)
+--E 78
+
+--S 79 of 1406
+m0:=a0-r0
+--R
+--R
+--R 3
+--R B a
+--R (4) - ----
+--R 6b
+--R Type: Expression(Integer)
+--E 79
+
+--S 80 of 1406
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 80
+
+)clear all
+
+--S 81 of 1406
+t0:=(a+b*x^2)^2*(A+B*x^2)/x^2
+--R
+--R
+--R 2 6 2 4 2 2 2
+--R B b x + (A b + 2B a b)x + (2A a b + B a )x + A a
+--R (1) -----------------------------------------------------
+--R 2
+--R x
+--R Type: Fraction(Polynomial(Integer))
+--E 81
+
+--S 82 of 1406
+r0:=-a^2*A/x+a*(2*A*b+a*B)*x+1/3*b*(A*b+2*a*B)*x^3+1/5*b^2*B*x^5
+--R
+--R
+--R 2 6 2 4 2 2 2
+--R 3B b x + (5A b + 10B a b)x + (30A a b + 15B a )x - 15A a
+--R (2) -------------------------------------------------------------
+--R 15x
+--R Type: Fraction(Polynomial(Integer))
+--E 82
+
+--S 83 of 1406
+a0:=integrate(t0,x)
+--R
+--R
+--R 2 6 2 4 2 2 2
+--R 3B b x + (5A b + 10B a b)x + (30A a b + 15B a )x - 15A a
+--R (3) -------------------------------------------------------------
+--R 15x
+--R Type: Union(Expression(Integer),...)
+--E 83
+
+--S 84 of 1406
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 84
+
+--S 85 of 1406
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 85
+
+)clear all
+
+--S 86 of 1406
+t0:=(a+b*x^2)^2*(A+B*x^2)/x^3
+--R
+--R
+--R 2 6 2 4 2 2 2
+--R B b x + (A b + 2B a b)x + (2A a b + B a )x + A a
+--R (1) -----------------------------------------------------
+--R 3
+--R x
+--R Type: Fraction(Polynomial(Integer))
+--E 86
+
+--S 87 of 1406
+r0:=-1/2*a^2*A/x^2+1/2*b*(A*b+2*a*B)*x^2+1/4*b^2*B*x^4+a*(2*A*b+a*B)*log(x)
+--R
+--R
+--R 2 2 2 6 2 4 2
+--R (8A a b + 4B a )x log(x) + B b x + (2A b + 4B a b)x - 2A a
+--R (2) --------------------------------------------------------------
+--R 2
+--R 4x
+--R Type: Expression(Integer)
+--E 87
+
+--S 88 of 1406
+a0:=integrate(t0,x)
+--R
+--R
+--R 2 2 2 6 2 4 2
+--R (8A a b + 4B a )x log(x) + B b x + (2A b + 4B a b)x - 2A a
+--R (3) --------------------------------------------------------------
+--R 2
+--R 4x
+--R Type: Union(Expression(Integer),...)
+--E 88
+
+--S 89 of 1406
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 89
+
+--S 90 of 1406
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 90
+
+)clear all
+
+--S 91 of 1406
+t0:=(a+b*x^2)^2*(A+B*x^2)/x^4
+--R
+--R
+--R 2 6 2 4 2 2 2
+--R B b x + (A b + 2B a b)x + (2A a b + B a )x + A a
+--R (1) -----------------------------------------------------
+--R 4
+--R x
+--R Type: Fraction(Polynomial(Integer))
+--E 91
+
+--S 92 of 1406
+r0:=-1/3*a^2*A/x^3-a*(2*A*b+a*B)/x+b*(A*b+2*a*B)*x+1/3*b^2*B*x^3
+--R
+--R
+--R 1 2 6 2 4 2 2 1 2
+--R - B b x + (A b + 2B a b)x + (- 2A a b - B a )x - - A a
+--R 3 3
+--R (2) -----------------------------------------------------------
+--R 3
+--R x
+--R Type: Fraction(Polynomial(Fraction(Integer)))
+--E 92
+
+--S 93 of 1406
+a0:=integrate(t0,x)
+--R
+--R
+--R 2 6 2 4 2 2 2
+--R B b x + (3A b + 6B a b)x + (- 6A a b - 3B a )x - A a
+--R (3) ---------------------------------------------------------
+--R 3
+--R 3x
+--R Type: Union(Expression(Integer),...)
+--E 93
+
+--S 94 of 1406
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 94
+
+--S 95 of 1406
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 95
+
+)clear all
+
+--S 96 of 1406
+t0:=(a+b*x^2)^2*(A+B*x^2)/x^5
+--R
+--R
+--R 2 6 2 4 2 2 2
+--R B b x + (A b + 2B a b)x + (2A a b + B a )x + A a
+--R (1) -----------------------------------------------------
+--R 5
+--R x
+--R Type: Fraction(Polynomial(Integer))
+--E 96
+
+--S 97 of 1406
+r0:=-1/4*a^2*A/x^4-1/2*a*(2*A*b+a*B)/x^2+1/2*b^2*B*x^2+b*(A*b+2*a*B)*log(x)
+--R
+--R
+--R 2 4 2 6 2 2 2
+--R (4A b + 8B a b)x log(x) + 2B b x + (- 4A a b - 2B a )x - A a
+--R (2) ----------------------------------------------------------------
+--R 4
+--R 4x
+--R Type: Expression(Integer)
+--E 97
+
+--S 98 of 1406
+a0:=integrate(t0,x)
+--R
+--R
+--R 2 4 2 6 2 2 2
+--R (4A b + 8B a b)x log(x) + 2B b x + (- 4A a b - 2B a )x - A a
+--R (3) ----------------------------------------------------------------
+--R 4
+--R 4x
+--R Type: Union(Expression(Integer),...)
+--E 98
+
+--S 99 of 1406
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 99
+
+--S 100 of 1406
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 100
+
+)clear all
+
+--S 101 of 1406
+t0:=(a+b*x^2)^2*(A+B*x^2)/x^6
+--R
+--R
+--R 2 6 2 4 2 2 2
+--R B b x + (A b + 2B a b)x + (2A a b + B a )x + A a
+--R (1) -----------------------------------------------------
+--R 6
+--R x
+--R Type: Fraction(Polynomial(Integer))
+--E 101
+
+--S 102 of 1406
+r0:=-1/5*a^2*A/x^5-1/3*a*(2*A*b+a*B)/x^3-b*(A*b+2*a*B)/x+b^2*B*x
+--R
+--R
+--R 2 6 2 4 2 1 2 2 1 2
+--R B b x + (- A b - 2B a b)x + (- - A a b - - B a )x - - A a
+--R 3 3 5
+--R (2) --------------------------------------------------------------
+--R 5
+--R x
+--R Type: Fraction(Polynomial(Fraction(Integer)))
+--E 102
+
+--S 103 of 1406
+a0:=integrate(t0,x)
+--R
+--R
+--R 2 6 2 4 2 2 2
+--R 15B b x + (- 15A b - 30B a b)x + (- 10A a b - 5B a )x - 3A a
+--R (3) -----------------------------------------------------------------
+--R 5
+--R 15x
+--R Type: Union(Expression(Integer),...)
+--E 103
+
+--S 104 of 1406
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 104
+
+--S 105 of 1406
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 105
+
+)clear all
+
+--S 106 of 1406
+t0:=(a+b*x^2)^2*(A+B*x^2)/x^7
+--R
+--R
+--R 2 6 2 4 2 2 2
+--R B b x + (A b + 2B a b)x + (2A a b + B a )x + A a
+--R (1) -----------------------------------------------------
+--R 7
+--R x
+--R Type: Fraction(Polynomial(Integer))
+--E 106
+
+--S 107 of 1406
+r0:=-1/4*a^2*B/x^4-a*b*B/x^2-1/6*A*(a+b*x^2)^3/(a*x^6)+b^2*B*log(x)
+--R
+--R
+--R (2)
+--R 2 6 3 6 2 2 4
+--R 12B a b x log(x) - 2A b x + (- 6A a b - 12B a b)x
+--R +
+--R 2 3 2 3
+--R (- 6A a b - 3B a )x - 2A a
+--R /
+--R 6
+--R 12a x
+--R Type: Expression(Integer)
+--E 107
+
+--S 108 of 1406
+a0:=integrate(t0,x)
+--R
+--R
+--R 2 6 2 4 2 2 2
+--R 12B b x log(x) + (- 6A b - 12B a b)x + (- 6A a b - 3B a )x - 2A a
+--R (3) ---------------------------------------------------------------------
+--R 6
+--R 12x
+--R Type: Union(Expression(Integer),...)
+--E 108
+
+--S 109 of 1406
+m0:=a0-r0
+--R
+--R
+--R 3
+--R A b
+--R (4) ----
+--R 6a
+--R Type: Expression(Integer)
+--E 109
+
+--S 110 of 1406
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 110
+
+)clear all
+
+--S 111 of 1406
+t0:=(a+b*x^2)^2*(A+B*x^2)/x^8
+--R
+--R
+--R 2 6 2 4 2 2 2
+--R B b x + (A b + 2B a b)x + (2A a b + B a )x + A a
+--R (1) -----------------------------------------------------
+--R 8
+--R x
+--R Type: Fraction(Polynomial(Integer))
+--E 111
+
+--S 112 of 1406
+r0:=-1/7*a^2*A/x^7-1/5*a*(2*A*b+a*B)/x^5-1/3*b*(A*b+2*a*B)/x^3-b^2*B/x
+--R
+--R
+--R 2 6 1 2 2 4 2 1 2 2 1 2
+--R - B b x + (- - A b - - B a b)x + (- - A a b - - B a )x - - A a
+--R 3 3 5 5 7
+--R (2) -------------------------------------------------------------------
+--R 7
+--R x
+--R Type: Fraction(Polynomial(Fraction(Integer)))
+--E 112
+
+--S 113 of 1406
+a0:=integrate(t0,x)
+--R
+--R
+--R 2 6 2 4 2 2 2
+--R - 105B b x + (- 35A b - 70B a b)x + (- 42A a b - 21B a )x - 15A a
+--R (3) ----------------------------------------------------------------------
+--R 7
+--R 105x
+--R Type: Union(Expression(Integer),...)
+--E 113
+
+--S 114 of 1406
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 114
+
+--S 115 of 1406
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 115
+
+)clear all
+
+--S 116 of 1406
+t0:=(a+b*x^2)^2*(A+B*x^2)/x^9
+--R
+--R
+--R 2 6 2 4 2 2 2
+--R B b x + (A b + 2B a b)x + (2A a b + B a )x + A a
+--R (1) -----------------------------------------------------
+--R 9
+--R x
+--R Type: Fraction(Polynomial(Integer))
+--E 116
+
+--S 117 of 1406
+r0:=-1/8*A*(a+b*x^2)^3/(a*x^8)+1/24*(A*b-4*a*B)*(a+b*x^2)^3/(a^2*x^6)
+--R
+--R
+--R (2)
+--R 1 4 1 3 8 1 2 2 6 1 2 2 1 3 4
+--R (-- A b - - B a b )x - - B a b x + (- - A a b - - B a b)x
+--R 24 6 2 4 2
+--R +
+--R 1 3 1 4 2 1 4
+--R (- - A a b - - B a )x - - A a
+--R 3 6 8
+--R /
+--R 2 8
+--R a x
+--R Type: Fraction(Polynomial(Fraction(Integer)))
+--E 117
+
+--S 118 of 1406
+a0:=integrate(t0,x)
+--R
+--R
+--R 2 6 2 4 2 2 2
+--R - 12B b x + (- 6A b - 12B a b)x + (- 8A a b - 4B a )x - 3A a
+--R (3) -----------------------------------------------------------------
+--R 8
+--R 24x
+--R Type: Union(Expression(Integer),...)
+--E 118
+
+--S 119 of 1406
+m0:=a0-r0
+--R
+--R
+--R 4 3
+--R - A b + 4B a b
+--R (4) ----------------
+--R 2
+--R 24a
+--R Type: Expression(Integer)
+--E 119
+
+--S 120 of 1406
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 120
+
+)clear all
+
+--S 121 of 1406
+t0:=x^m*(a+b*x^2)^5*(A+B*x^2)
+--R
+--R
+--R (1)
+--R 5 12 5 4 10 4 2 3 8
+--R B b x + (A b + 5B a b )x + (5A a b + 10B a b )x
+--R +
+--R 2 3 3 2 6 3 2 4 4 4 5 2 5
+--R (10A a b + 10B a b )x + (10A a b + 5B a b)x + (5A a b + B a )x + A a
+--R *
+--R m
+--R x
+--R Type: Expression(Integer)
+--E 121
+
+--S 122 of 1406
+r0:=a^5*A*x^(1+m)/(1+m)+a^4*(5*A*b+a*B)*x^(3+m)/(3+m)+5*a^3*b*_
+ (2*A*b+a*B)*x^(5+m)/(5+m)+10*a^2*b^2*(A*b+a*B)*x^(7+m)/_
+ (7+m)+5*a*b^3*(A*b+2*a*B)*x^(9+m)/(9+m)+b^4*(A*b+5*a*B)*_
+ x^(11+m)/(11+m)+b^5*B*x^(13+m)/(13+m)
+--R
+--R
+--R (2)
+--R 5 6 5 5 5 4 5 3 5 2 5
+--R B b m + 36B b m + 505B b m + 3480B b m + 12139B b m + 19524B b m
+--R +
+--R 5
+--R 10395B b
+--R *
+--R m + 13
+--R x
+--R +
+--R 5 4 6 5 4 5
+--R (A b + 5B a b )m + (38A b + 190B a b )m
+--R +
+--R 5 4 4 5 4 3
+--R (555A b + 2775B a b )m + (3940A b + 19700B a b )m
+--R +
+--R 5 4 2 5 4 5
+--R (14039A b + 70195B a b )m + (22902A b + 114510B a b )m + 12285A b
+--R +
+--R 4
+--R 61425B a b
+--R *
+--R m + 11
+--R x
+--R +
+--R 4 2 3 6 4 2 3 5
+--R (5A a b + 10B a b )m + (200A a b + 400B a b )m
+--R +
+--R 4 2 3 4 4 2 3 3
+--R (3065A a b + 6130B a b )m + (22640A a b + 45280B a b )m
+--R +
+--R 4 2 3 2 4 2 3
+--R (83135A a b + 166270B a b )m + (138440A a b + 276880B a b )m
+--R +
+--R 4 2 3
+--R 75075A a b + 150150B a b
+--R *
+--R m + 9
+--R x
+--R +
+--R 2 3 3 2 6 2 3 3 2 5
+--R (10A a b + 10B a b )m + (420A a b + 420B a b )m
+--R +
+--R 2 3 3 2 4 2 3 3 2 3
+--R (6790A a b + 6790B a b )m + (52920A a b + 52920B a b )m
+--R +
+--R 2 3 3 2 2 2 3 3 2
+--R (203350A a b + 203350B a b )m + (349860A a b + 349860B a b )m
+--R +
+--R 2 3 3 2
+--R 193050A a b + 193050B a b
+--R *
+--R m + 7
+--R x
+--R +
+--R 3 2 4 6 3 2 4 5
+--R (10A a b + 5B a b)m + (440A a b + 220B a b)m
+--R +
+--R 3 2 4 4 3 2 4 3
+--R (7530A a b + 3765B a b)m + (62800A a b + 31400B a b)m
+--R +
+--R 3 2 4 2 3 2 4
+--R (259790A a b + 129895B a b)m + (474360A a b + 237180B a b)m
+--R +
+--R 3 2 4
+--R 270270A a b + 135135B a b
+--R *
+--R m + 5
+--R x
+--R +
+--R 4 5 6 4 5 5 4 5 4
+--R (5A a b + B a )m + (230A a b + 46B a )m + (4175A a b + 835B a )m
+--R +
+--R 4 5 3 4 5 2
+--R (37700A a b + 7540B a )m + (173795A a b + 34759B a )m
+--R +
+--R 4 5 4 5
+--R (365270A a b + 73054B a )m + 225225A a b + 45045B a
+--R *
+--R m + 3
+--R x
+--R +
+--R 5 6 5 5 5 4 5 3 5 2
+--R A a m + 48A a m + 925A a m + 9120A a m + 48259A a m
+--R +
+--R 5 5
+--R 129072A a m + 135135A a
+--R *
+--R m + 1
+--R x
+--R /
+--R 7 6 5 4 3 2
+--R m + 49m + 973m + 10045m + 57379m + 177331m + 264207m + 135135
+--R Type: Expression(Integer)
+--E 122
+
+--S 123 of 1406
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 5 6 5 5 5 4 5 3 5 2
+--R B b m + 36B b m + 505B b m + 3480B b m + 12139B b m
+--R +
+--R 5 5
+--R 19524B b m + 10395B b
+--R *
+--R 13
+--R x
+--R +
+--R 5 4 6 5 4 5
+--R (A b + 5B a b )m + (38A b + 190B a b )m
+--R +
+--R 5 4 4 5 4 3
+--R (555A b + 2775B a b )m + (3940A b + 19700B a b )m
+--R +
+--R 5 4 2 5 4
+--R (14039A b + 70195B a b )m + (22902A b + 114510B a b )m
+--R +
+--R 5 4
+--R 12285A b + 61425B a b
+--R *
+--R 11
+--R x
+--R +
+--R 4 2 3 6 4 2 3 5
+--R (5A a b + 10B a b )m + (200A a b + 400B a b )m
+--R +
+--R 4 2 3 4 4 2 3 3
+--R (3065A a b + 6130B a b )m + (22640A a b + 45280B a b )m
+--R +
+--R 4 2 3 2 4 2 3
+--R (83135A a b + 166270B a b )m + (138440A a b + 276880B a b )m
+--R +
+--R 4 2 3
+--R 75075A a b + 150150B a b
+--R *
+--R 9
+--R x
+--R +
+--R 2 3 3 2 6 2 3 3 2 5
+--R (10A a b + 10B a b )m + (420A a b + 420B a b )m
+--R +
+--R 2 3 3 2 4 2 3 3 2 3
+--R (6790A a b + 6790B a b )m + (52920A a b + 52920B a b )m
+--R +
+--R 2 3 3 2 2 2 3 3 2
+--R (203350A a b + 203350B a b )m + (349860A a b + 349860B a b )m
+--R +
+--R 2 3 3 2
+--R 193050A a b + 193050B a b
+--R *
+--R 7
+--R x
+--R +
+--R 3 2 4 6 3 2 4 5
+--R (10A a b + 5B a b)m + (440A a b + 220B a b)m
+--R +
+--R 3 2 4 4 3 2 4 3
+--R (7530A a b + 3765B a b)m + (62800A a b + 31400B a b)m
+--R +
+--R 3 2 4 2 3 2 4
+--R (259790A a b + 129895B a b)m + (474360A a b + 237180B a b)m
+--R +
+--R 3 2 4
+--R 270270A a b + 135135B a b
+--R *
+--R 5
+--R x
+--R +
+--R 4 5 6 4 5 5 4 5 4
+--R (5A a b + B a )m + (230A a b + 46B a )m + (4175A a b + 835B a )m
+--R +
+--R 4 5 3 4 5 2
+--R (37700A a b + 7540B a )m + (173795A a b + 34759B a )m
+--R +
+--R 4 5 4 5
+--R (365270A a b + 73054B a )m + 225225A a b + 45045B a
+--R *
+--R 3
+--R x
+--R +
+--R 5 6 5 5 5 4 5 3 5 2
+--R A a m + 48A a m + 925A a m + 9120A a m + 48259A a m
+--R +
+--R 5 5
+--R 129072A a m + 135135A a
+--R *
+--R x
+--R *
+--R m log(x)
+--R %e
+--R /
+--R 7 6 5 4 3 2
+--R m + 49m + 973m + 10045m + 57379m + 177331m + 264207m + 135135
+--R Type: Union(Expression(Integer),...)
+--E 123
+
+--S 124 of 1406
+m0:=a0-r0
+--R
+--R
+--R (4)
+--R 5 6 5 5 5 4 5 3 5 2
+--R B b m + 36B b m + 505B b m + 3480B b m + 12139B b m
+--R +
+--R 5 5
+--R 19524B b m + 10395B b
+--R *
+--R 13
+--R x
+--R +
+--R 5 4 6 5 4 5
+--R (A b + 5B a b )m + (38A b + 190B a b )m
+--R +
+--R 5 4 4 5 4 3
+--R (555A b + 2775B a b )m + (3940A b + 19700B a b )m
+--R +
+--R 5 4 2 5 4
+--R (14039A b + 70195B a b )m + (22902A b + 114510B a b )m
+--R +
+--R 5 4
+--R 12285A b + 61425B a b
+--R *
+--R 11
+--R x
+--R +
+--R 4 2 3 6 4 2 3 5
+--R (5A a b + 10B a b )m + (200A a b + 400B a b )m
+--R +
+--R 4 2 3 4 4 2 3 3
+--R (3065A a b + 6130B a b )m + (22640A a b + 45280B a b )m
+--R +
+--R 4 2 3 2 4 2 3
+--R (83135A a b + 166270B a b )m + (138440A a b + 276880B a b )m
+--R +
+--R 4 2 3
+--R 75075A a b + 150150B a b
+--R *
+--R 9
+--R x
+--R +
+--R 2 3 3 2 6 2 3 3 2 5
+--R (10A a b + 10B a b )m + (420A a b + 420B a b )m
+--R +
+--R 2 3 3 2 4 2 3 3 2 3
+--R (6790A a b + 6790B a b )m + (52920A a b + 52920B a b )m
+--R +
+--R 2 3 3 2 2 2 3 3 2
+--R (203350A a b + 203350B a b )m + (349860A a b + 349860B a b )m
+--R +
+--R 2 3 3 2
+--R 193050A a b + 193050B a b
+--R *
+--R 7
+--R x
+--R +
+--R 3 2 4 6 3 2 4 5
+--R (10A a b + 5B a b)m + (440A a b + 220B a b)m
+--R +
+--R 3 2 4 4 3 2 4 3
+--R (7530A a b + 3765B a b)m + (62800A a b + 31400B a b)m
+--R +
+--R 3 2 4 2 3 2 4
+--R (259790A a b + 129895B a b)m + (474360A a b + 237180B a b)m
+--R +
+--R 3 2 4
+--R 270270A a b + 135135B a b
+--R *
+--R 5
+--R x
+--R +
+--R 4 5 6 4 5 5
+--R (5A a b + B a )m + (230A a b + 46B a )m
+--R +
+--R 4 5 4 4 5 3
+--R (4175A a b + 835B a )m + (37700A a b + 7540B a )m
+--R +
+--R 4 5 2 4 5
+--R (173795A a b + 34759B a )m + (365270A a b + 73054B a )m
+--R +
+--R 4 5
+--R 225225A a b + 45045B a
+--R *
+--R 3
+--R x
+--R +
+--R 5 6 5 5 5 4 5 3 5 2
+--R A a m + 48A a m + 925A a m + 9120A a m + 48259A a m
+--R +
+--R 5 5
+--R 129072A a m + 135135A a
+--R *
+--R x
+--R *
+--R m log(x)
+--R %e
+--R +
+--R 5 6 5 5 5 4 5 3 5 2
+--R - B b m - 36B b m - 505B b m - 3480B b m - 12139B b m
+--R +
+--R 5 5
+--R - 19524B b m - 10395B b
+--R *
+--R m + 13
+--R x
+--R +
+--R 5 4 6 5 4 5
+--R (- A b - 5B a b )m + (- 38A b - 190B a b )m
+--R +
+--R 5 4 4 5 4 3
+--R (- 555A b - 2775B a b )m + (- 3940A b - 19700B a b )m
+--R +
+--R 5 4 2 5 4
+--R (- 14039A b - 70195B a b )m + (- 22902A b - 114510B a b )m
+--R +
+--R 5 4
+--R - 12285A b - 61425B a b
+--R *
+--R m + 11
+--R x
+--R +
+--R 4 2 3 6 4 2 3 5
+--R (- 5A a b - 10B a b )m + (- 200A a b - 400B a b )m
+--R +
+--R 4 2 3 4 4 2 3 3
+--R (- 3065A a b - 6130B a b )m + (- 22640A a b - 45280B a b )m
+--R +
+--R 4 2 3 2 4 2 3
+--R (- 83135A a b - 166270B a b )m + (- 138440A a b - 276880B a b )m
+--R +
+--R 4 2 3
+--R - 75075A a b - 150150B a b
+--R *
+--R m + 9
+--R x
+--R +
+--R 2 3 3 2 6 2 3 3 2 5
+--R (- 10A a b - 10B a b )m + (- 420A a b - 420B a b )m
+--R +
+--R 2 3 3 2 4 2 3 3 2 3
+--R (- 6790A a b - 6790B a b )m + (- 52920A a b - 52920B a b )m
+--R +
+--R 2 3 3 2 2 2 3 3 2
+--R (- 203350A a b - 203350B a b )m + (- 349860A a b - 349860B a b )m
+--R +
+--R 2 3 3 2
+--R - 193050A a b - 193050B a b
+--R *
+--R m + 7
+--R x
+--R +
+--R 3 2 4 6 3 2 4 5
+--R (- 10A a b - 5B a b)m + (- 440A a b - 220B a b)m
+--R +
+--R 3 2 4 4 3 2 4 3
+--R (- 7530A a b - 3765B a b)m + (- 62800A a b - 31400B a b)m
+--R +
+--R 3 2 4 2 3 2 4
+--R (- 259790A a b - 129895B a b)m + (- 474360A a b - 237180B a b)m
+--R +
+--R 3 2 4
+--R - 270270A a b - 135135B a b
+--R *
+--R m + 5
+--R x
+--R +
+--R 4 5 6 4 5 5
+--R (- 5A a b - B a )m + (- 230A a b - 46B a )m
+--R +
+--R 4 5 4 4 5 3
+--R (- 4175A a b - 835B a )m + (- 37700A a b - 7540B a )m
+--R +
+--R 4 5 2 4 5
+--R (- 173795A a b - 34759B a )m + (- 365270A a b - 73054B a )m
+--R +
+--R 4 5
+--R - 225225A a b - 45045B a
+--R *
+--R m + 3
+--R x
+--R +
+--R 5 6 5 5 5 4 5 3 5 2
+--R - A a m - 48A a m - 925A a m - 9120A a m - 48259A a m
+--R +
+--R 5 5
+--R - 129072A a m - 135135A a
+--R *
+--R m + 1
+--R x
+--R /
+--R 7 6 5 4 3 2
+--R m + 49m + 973m + 10045m + 57379m + 177331m + 264207m + 135135
+--R Type: Expression(Integer)
+--E 124
+
+--S 125 of 1406
+d0:=normalize m0
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 125
+
+)clear all
+
+--S 126 of 1406
+t0:=x^9*(a+b*x^2)^5*(A+B*x^2)
+--R
+--R
+--R (1)
+--R 5 21 5 4 19 4 2 3 17
+--R B b x + (A b + 5B a b )x + (5A a b + 10B a b )x
+--R +
+--R 2 3 3 2 15 3 2 4 13 4 5 11
+--R (10A a b + 10B a b )x + (10A a b + 5B a b)x + (5A a b + B a )x
+--R +
+--R 5 9
+--R A a x
+--R Type: Polynomial(Integer)
+--E 126
+
+--S 127 of 1406
+r0:=1/10*a^5*A*x^10+1/12*a^4*(5*A*b+a*B)*x^12+5/14*a^3*b*(2*A*b+a*B)*_
+ x^14+5/8*a^2*b^2*(A*b+a*B)*x^16+5/18*a*b^3*(A*b+2*a*B)*x^18+_
+ 1/20*b^4*(A*b+5*a*B)*x^20+1/22*b^5*B*x^22
+--R
+--R
+--R (2)
+--R 1 5 22 1 5 1 4 20 5 4 5 2 3 18
+--R -- B b x + (-- A b + - B a b )x + (-- A a b + - B a b )x
+--R 22 20 4 18 9
+--R +
+--R 5 2 3 5 3 2 16 5 3 2 5 4 14
+--R (- A a b + - B a b )x + (- A a b + -- B a b)x
+--R 8 8 7 14
+--R +
+--R 5 4 1 5 12 1 5 10
+--R (-- A a b + -- B a )x + -- A a x
+--R 12 12 10
+--R Type: Polynomial(Fraction(Integer))
+--E 127
+
+--S 128 of 1406
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 1 5 22 1 5 1 4 20 5 4 5 2 3 18
+--R -- B b x + (-- A b + - B a b )x + (-- A a b + - B a b )x
+--R 22 20 4 18 9
+--R +
+--R 5 2 3 5 3 2 16 5 3 2 5 4 14
+--R (- A a b + - B a b )x + (- A a b + -- B a b)x
+--R 8 8 7 14
+--R +
+--R 5 4 1 5 12 1 5 10
+--R (-- A a b + -- B a )x + -- A a x
+--R 12 12 10
+--R Type: Polynomial(Fraction(Integer))
+--E 128
+
+--S 129 of 1406
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Polynomial(Fraction(Integer))
+--E 129
+
+--S 130 of 1406
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Polynomial(Fraction(Integer))
+--E 130
+
+)clear all
+
+--S 131 of 1406
+t0:=x^8*(a+b*x^2)^5*(A+B*x^2)
+--R
+--R
+--R (1)
+--R 5 20 5 4 18 4 2 3 16
+--R B b x + (A b + 5B a b )x + (5A a b + 10B a b )x
+--R +
+--R 2 3 3 2 14 3 2 4 12 4 5 10
+--R (10A a b + 10B a b )x + (10A a b + 5B a b)x + (5A a b + B a )x
+--R +
+--R 5 8
+--R A a x
+--R Type: Polynomial(Integer)
+--E 131
+
+--S 132 of 1406
+r0:=1/9*a^5*A*x^9+1/11*a^4*(5*A*b+a*B)*x^11+5/13*a^3*b*(2*A*b+a*B)*x^13+_
+ 2/3*a^2*b^2*(A*b+a*B)*x^15+5/17*a*b^3*(A*b+2*a*B)*x^17+_
+ 1/19*b^4*(A*b+5*a*B)*x^19+1/21*b^5*B*x^21
+--R
+--R
+--R (2)
+--R 1 5 21 1 5 5 4 19 5 4 10 2 3 17
+--R -- B b x + (-- A b + -- B a b )x + (-- A a b + -- B a b )x
+--R 21 19 19 17 17
+--R +
+--R 2 2 3 2 3 2 15 10 3 2 5 4 13
+--R (- A a b + - B a b )x + (-- A a b + -- B a b)x
+--R 3 3 13 13
+--R +
+--R 5 4 1 5 11 1 5 9
+--R (-- A a b + -- B a )x + - A a x
+--R 11 11 9
+--R Type: Polynomial(Fraction(Integer))
+--E 132
+
+--S 133 of 1406
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 1 5 21 1 5 5 4 19 5 4 10 2 3 17
+--R -- B b x + (-- A b + -- B a b )x + (-- A a b + -- B a b )x
+--R 21 19 19 17 17
+--R +
+--R 2 2 3 2 3 2 15 10 3 2 5 4 13
+--R (- A a b + - B a b )x + (-- A a b + -- B a b)x
+--R 3 3 13 13
+--R +
+--R 5 4 1 5 11 1 5 9
+--R (-- A a b + -- B a )x + - A a x
+--R 11 11 9
+--R Type: Polynomial(Fraction(Integer))
+--E 133
+
+--S 134 of 1406
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Polynomial(Fraction(Integer))
+--E 134
+
+--S 135 of 1406
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Polynomial(Fraction(Integer))
+--E 135
+
+)clear all
+
+--S 136 of 1406
+t0:=x^7*(a+b*x^2)^5*(A+B*x^2)
+--R
+--R
+--R (1)
+--R 5 19 5 4 17 4 2 3 15
+--R B b x + (A b + 5B a b )x + (5A a b + 10B a b )x
+--R +
+--R 2 3 3 2 13 3 2 4 11 4 5 9
+--R (10A a b + 10B a b )x + (10A a b + 5B a b)x + (5A a b + B a )x
+--R +
+--R 5 7
+--R A a x
+--R Type: Polynomial(Integer)
+--E 136
+
+--S 137 of 1406
+r0:=1/8*a^5*A*x^8+1/10*a^4*(5*A*b+a*B)*x^10+5/12*a^3*b*(2*A*b+a*B)*x^12+_
+ 5/7*a^2*b^2*(A*b+a*B)*x^14+5/16*a*b^3*(A*b+2*a*B)*x^16+_
+ 1/18*b^4*(A*b+5*a*B)*x^18+1/20*b^5*B*x^20
+--R
+--R
+--R (2)
+--R 1 5 20 1 5 5 4 18 5 4 5 2 3 16
+--R -- B b x + (-- A b + -- B a b )x + (-- A a b + - B a b )x
+--R 20 18 18 16 8
+--R +
+--R 5 2 3 5 3 2 14 5 3 2 5 4 12
+--R (- A a b + - B a b )x + (- A a b + -- B a b)x
+--R 7 7 6 12
+--R +
+--R 1 4 1 5 10 1 5 8
+--R (- A a b + -- B a )x + - A a x
+--R 2 10 8
+--R Type: Polynomial(Fraction(Integer))
+--E 137
+
+--S 138 of 1406
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 1 5 20 1 5 5 4 18 5 4 5 2 3 16
+--R -- B b x + (-- A b + -- B a b )x + (-- A a b + - B a b )x
+--R 20 18 18 16 8
+--R +
+--R 5 2 3 5 3 2 14 5 3 2 5 4 12
+--R (- A a b + - B a b )x + (- A a b + -- B a b)x
+--R 7 7 6 12
+--R +
+--R 1 4 1 5 10 1 5 8
+--R (- A a b + -- B a )x + - A a x
+--R 2 10 8
+--R Type: Polynomial(Fraction(Integer))
+--E 138
+
+--S 139 of 1406
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Polynomial(Fraction(Integer))
+--E 139
+
+--S 140 of 1406
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Polynomial(Fraction(Integer))
+--E 140
+
+)clear all
+
+--S 141 of 1406
+t0:=x^6*(a+b*x^2)^5*(A+B*x^2)
+--R
+--R
+--R (1)
+--R 5 18 5 4 16 4 2 3 14
+--R B b x + (A b + 5B a b )x + (5A a b + 10B a b )x
+--R +
+--R 2 3 3 2 12 3 2 4 10 4 5 8
+--R (10A a b + 10B a b )x + (10A a b + 5B a b)x + (5A a b + B a )x
+--R +
+--R 5 6
+--R A a x
+--R Type: Polynomial(Integer)
+--E 141
+
+--S 142 of 1406
+r0:=1/7*a^5*A*x^7+1/9*a^4*(5*A*b+a*B)*x^9+5/11*a^3*b*(2*A*b+a*B)*x^11+_
+ 10/13*a^2*b^2*(A*b+a*B)*x^13+1/3*a*b^3*(A*b+2*a*B)*x^15+_
+ 1/17*b^4*(A*b+5*a*B)*x^17+1/19*b^5*B*x^19
+--R
+--R
+--R (2)
+--R 1 5 19 1 5 5 4 17 1 4 2 2 3 15
+--R -- B b x + (-- A b + -- B a b )x + (- A a b + - B a b )x
+--R 19 17 17 3 3
+--R +
+--R 10 2 3 10 3 2 13 10 3 2 5 4 11
+--R (-- A a b + -- B a b )x + (-- A a b + -- B a b)x
+--R 13 13 11 11
+--R +
+--R 5 4 1 5 9 1 5 7
+--R (- A a b + - B a )x + - A a x
+--R 9 9 7
+--R Type: Polynomial(Fraction(Integer))
+--E 142
+
+--S 143 of 1406
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 1 5 19 1 5 5 4 17 1 4 2 2 3 15
+--R -- B b x + (-- A b + -- B a b )x + (- A a b + - B a b )x
+--R 19 17 17 3 3
+--R +
+--R 10 2 3 10 3 2 13 10 3 2 5 4 11
+--R (-- A a b + -- B a b )x + (-- A a b + -- B a b)x
+--R 13 13 11 11
+--R +
+--R 5 4 1 5 9 1 5 7
+--R (- A a b + - B a )x + - A a x
+--R 9 9 7
+--R Type: Polynomial(Fraction(Integer))
+--E 143
+
+--S 144 of 1406
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Polynomial(Fraction(Integer))
+--E 144
+
+--S 145 of 1406
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Polynomial(Fraction(Integer))
+--E 145
+
+)clear all
+
+--S 146 of 1406
+t0:=x^5*(a+b*x^2)^5*(A+B*x^2)
+--R
+--R
+--R (1)
+--R 5 17 5 4 15 4 2 3 13
+--R B b x + (A b + 5B a b )x + (5A a b + 10B a b )x
+--R +
+--R 2 3 3 2 11 3 2 4 9 4 5 7 5 5
+--R (10A a b + 10B a b )x + (10A a b + 5B a b)x + (5A a b + B a )x + A a x
+--R Type: Polynomial(Integer)
+--E 146
+
+--S 147 of 1406
+r0:=1/12*a^2*(A*b-a*B)*(a+b*x^2)^6/b^4-1/14*a*(2*A*b-3*a*B)*(a+b*x^2)^7/_
+ b^4+1/16*(A*b-3*a*B)*(a+b*x^2)^8/b^4+1/18*B*(a+b*x^2)^9/b^4
+--R
+--R
+--R (2)
+--R 1 9 18 1 9 5 8 16 5 8 5 2 7 14
+--R -- B b x + (-- A b + -- B a b )x + (-- A a b + - B a b )x
+--R 18 16 16 14 7
+--R +
+--R 5 2 7 5 3 6 12 3 6 1 4 5 10
+--R (- A a b + - B a b )x + (A a b + - B a b )x
+--R 6 6 2
+--R +
+--R 5 4 5 1 5 4 8 1 5 4 6 1 8 1 9
+--R (- A a b + - B a b )x + - A a b x + --- A a b - ---- B a
+--R 8 8 6 336 1008
+--R /
+--R 4
+--R b
+--R Type: Fraction(Polynomial(Fraction(Integer)))
+--E 147
+
+--S 148 of 1406
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 1 5 18 1 5 5 4 16 5 4 5 2 3 14
+--R -- B b x + (-- A b + -- B a b )x + (-- A a b + - B a b )x
+--R 18 16 16 14 7
+--R +
+--R 5 2 3 5 3 2 12 3 2 1 4 10 5 4 1 5 8
+--R (- A a b + - B a b )x + (A a b + - B a b)x + (- A a b + - B a )x
+--R 6 6 2 8 8
+--R +
+--R 1 5 6
+--R - A a x
+--R 6
+--R Type: Polynomial(Fraction(Integer))
+--E 148
+
+--S 149 of 1406
+m0:=a0-r0
+--R
+--R
+--R 1 8 1 9
+--R - --- A a b + ---- B a
+--R 336 1008
+--R (4) -----------------------
+--R 4
+--R b
+--R Type: Fraction(Polynomial(Fraction(Integer)))
+--E 149
+
+--S 150 of 1406
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Fraction(Polynomial(Fraction(Integer)))
+--E 150
+
+)clear all
+
+--S 151 of 1406
+t0:=x^4*(a+b*x^2)^5*(A+B*x^2)
+--R
+--R
+--R (1)
+--R 5 16 5 4 14 4 2 3 12
+--R B b x + (A b + 5B a b )x + (5A a b + 10B a b )x
+--R +
+--R 2 3 3 2 10 3 2 4 8 4 5 6 5 4
+--R (10A a b + 10B a b )x + (10A a b + 5B a b)x + (5A a b + B a )x + A a x
+--R Type: Polynomial(Integer)
+--E 151
+
+--S 152 of 1406
+r0:=1/5*a^5*A*x^5+1/7*a^4*(5*A*b+a*B)*x^7+5/9*a^3*b*(2*A*b+a*B)*x^9+_
+ 10/11*a^2*b^2*(A*b+a*B)*x^11+5/13*a*b^3*(A*b+2*a*B)*x^13+_
+ 1/15*b^4*(A*b+5*a*B)*x^15+1/17*b^5*B*x^17
+--R
+--R
+--R (2)
+--R 1 5 17 1 5 1 4 15 5 4 10 2 3 13
+--R -- B b x + (-- A b + - B a b )x + (-- A a b + -- B a b )x
+--R 17 15 3 13 13
+--R +
+--R 10 2 3 10 3 2 11 10 3 2 5 4 9 5 4 1 5 7
+--R (-- A a b + -- B a b )x + (-- A a b + - B a b)x + (- A a b + - B a )x
+--R 11 11 9 9 7 7
+--R +
+--R 1 5 5
+--R - A a x
+--R 5
+--R Type: Polynomial(Fraction(Integer))
+--E 152
+
+--S 153 of 1406
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 1 5 17 1 5 1 4 15 5 4 10 2 3 13
+--R -- B b x + (-- A b + - B a b )x + (-- A a b + -- B a b )x
+--R 17 15 3 13 13
+--R +
+--R 10 2 3 10 3 2 11 10 3 2 5 4 9 5 4 1 5 7
+--R (-- A a b + -- B a b )x + (-- A a b + - B a b)x + (- A a b + - B a )x
+--R 11 11 9 9 7 7
+--R +
+--R 1 5 5
+--R - A a x
+--R 5
+--R Type: Polynomial(Fraction(Integer))
+--E 153
+
+--S 154 of 1406
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Polynomial(Fraction(Integer))
+--E 154
+
+--S 155 of 1406
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Polynomial(Fraction(Integer))
+--E 155
+
+)clear all
+
+--S 156 of 1406
+t0:=x^3*(a+b*x^2)^5*(A+B*x^2)
+--R
+--R
+--R (1)
+--R 5 15 5 4 13 4 2 3 11
+--R B b x + (A b + 5B a b )x + (5A a b + 10B a b )x
+--R +
+--R 2 3 3 2 9 3 2 4 7 4 5 5 5 3
+--R (10A a b + 10B a b )x + (10A a b + 5B a b)x + (5A a b + B a )x + A a x
+--R Type: Polynomial(Integer)
+--E 156
+
+--S 157 of 1406
+r0:=-1/12*a*(A*b-a*B)*(a+b*x^2)^6/b^3+1/14*(A*b-2*a*B)*(a+b*x^2)^7/b^3+_
+ 1/16*B*(a+b*x^2)^8/b^3
+--R
+--R
+--R (2)
+--R 1 8 16 1 8 5 7 14 5 7 5 2 6 12
+--R -- B b x + (-- A b + -- B a b )x + (-- A a b + - B a b )x
+--R 16 14 14 12 6
+--R +
+--R 2 6 3 5 10 5 3 5 5 4 4 8 5 4 4 1 5 3 6
+--R (A a b + B a b )x + (- A a b + - B a b )x + (- A a b + - B a b )x
+--R 4 8 6 6
+--R +
+--R 1 5 3 4 1 7 1 8
+--R - A a b x - -- A a b + --- B a
+--R 4 84 336
+--R /
+--R 3
+--R b
+--R Type: Fraction(Polynomial(Fraction(Integer)))
+--E 157
+
+--S 158 of 1406
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 1 5 16 1 5 5 4 14 5 4 5 2 3 12
+--R -- B b x + (-- A b + -- B a b )x + (-- A a b + - B a b )x
+--R 16 14 14 12 6
+--R +
+--R 2 3 3 2 10 5 3 2 5 4 8 5 4 1 5 6
+--R (A a b + B a b )x + (- A a b + - B a b)x + (- A a b + - B a )x
+--R 4 8 6 6
+--R +
+--R 1 5 4
+--R - A a x
+--R 4
+--R Type: Polynomial(Fraction(Integer))
+--E 158
+
+--S 159 of 1406
+m0:=a0-r0
+--R
+--R
+--R 1 7 1 8
+--R -- A a b - --- B a
+--R 84 336
+--R (4) -------------------
+--R 3
+--R b
+--R Type: Fraction(Polynomial(Fraction(Integer)))
+--E 159
+
+--S 160 of 1406
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Fraction(Polynomial(Fraction(Integer)))
+--E 160
+
+)clear all
+
+--S 161 of 1406
+t0:=x^2*(a+b*x^2)^5*(A+B*x^2)
+--R
+--R
+--R (1)
+--R 5 14 5 4 12 4 2 3 10
+--R B b x + (A b + 5B a b )x + (5A a b + 10B a b )x
+--R +
+--R 2 3 3 2 8 3 2 4 6 4 5 4 5 2
+--R (10A a b + 10B a b )x + (10A a b + 5B a b)x + (5A a b + B a )x + A a x
+--R Type: Polynomial(Integer)
+--E 161
+
+--S 162 of 1406
+r0:=1/3*a^5*A*x^3+1/5*a^4*(5*A*b+a*B)*x^5+5/7*a^3*b*(2*A*b+a*B)*x^7+_
+ 10/9*a^2*b^2*(A*b+a*B)*x^9+5/11*a*b^3*(A*b+2*a*B)*x^11+_
+ 1/13*b^4*(A*b+5*a*B)*x^13+1/15*b^5*B*x^15
+--R
+--R
+--R (2)
+--R 1 5 15 1 5 5 4 13 5 4 10 2 3 11
+--R -- B b x + (-- A b + -- B a b )x + (-- A a b + -- B a b )x
+--R 15 13 13 11 11
+--R +
+--R 10 2 3 10 3 2 9 10 3 2 5 4 7 4 1 5 5
+--R (-- A a b + -- B a b )x + (-- A a b + - B a b)x + (A a b + - B a )x
+--R 9 9 7 7 5
+--R +
+--R 1 5 3
+--R - A a x
+--R 3
+--R Type: Polynomial(Fraction(Integer))
+--E 162
+
+--S 163 of 1406
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 1 5 15 1 5 5 4 13 5 4 10 2 3 11
+--R -- B b x + (-- A b + -- B a b )x + (-- A a b + -- B a b )x
+--R 15 13 13 11 11
+--R +
+--R 10 2 3 10 3 2 9 10 3 2 5 4 7 4 1 5 5
+--R (-- A a b + -- B a b )x + (-- A a b + - B a b)x + (A a b + - B a )x
+--R 9 9 7 7 5
+--R +
+--R 1 5 3
+--R - A a x
+--R 3
+--R Type: Polynomial(Fraction(Integer))
+--E 163
+
+--S 164 of 1406
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Polynomial(Fraction(Integer))
+--E 164
+
+--S 165 of 1406
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Polynomial(Fraction(Integer))
+--E 165
+
+)clear all
+
+--S 166 of 1406
+t0:=x*(a+b*x^2)^5*(A+B*x^2)
+--R
+--R
+--R (1)
+--R 5 13 5 4 11 4 2 3 9
+--R B b x + (A b + 5B a b )x + (5A a b + 10B a b )x
+--R +
+--R 2 3 3 2 7 3 2 4 5 4 5 3 5
+--R (10A a b + 10B a b )x + (10A a b + 5B a b)x + (5A a b + B a )x + A a x
+--R Type: Polynomial(Integer)
+--E 166
+
+--S 167 of 1406
+r0:=1/12*(A*b-a*B)*(a+b*x^2)^6/b^2+1/14*B*(a+b*x^2)^7/b^2
+--R
+--R
+--R (2)
+--R 1 7 14 1 7 5 6 12 1 6 2 5 10
+--R -- B b x + (-- A b + -- B a b )x + (- A a b + B a b )x
+--R 14 12 12 2
+--R +
+--R 5 2 5 5 3 4 8 5 3 4 5 4 3 6
+--R (- A a b + - B a b )x + (- A a b + - B a b )x
+--R 4 4 3 6
+--R +
+--R 5 4 3 1 5 2 4 1 5 2 2 1 6 1 7
+--R (- A a b + - B a b )x + - A a b x + -- A a b - -- B a
+--R 4 4 2 12 84
+--R /
+--R 2
+--R b
+--R Type: Fraction(Polynomial(Fraction(Integer)))
+--E 167
+
+--S 168 of 1406
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 1 5 14 1 5 5 4 12 1 4 2 3 10
+--R -- B b x + (-- A b + -- B a b )x + (- A a b + B a b )x
+--R 14 12 12 2
+--R +
+--R 5 2 3 5 3 2 8 5 3 2 5 4 6 5 4 1 5 4
+--R (- A a b + - B a b )x + (- A a b + - B a b)x + (- A a b + - B a )x
+--R 4 4 3 6 4 4
+--R +
+--R 1 5 2
+--R - A a x
+--R 2
+--R Type: Polynomial(Fraction(Integer))
+--E 168
+
+--S 169 of 1406
+m0:=a0-r0
+--R
+--R
+--R 1 6 1 7
+--R - -- A a b + -- B a
+--R 12 84
+--R (4) --------------------
+--R 2
+--R b
+--R Type: Fraction(Polynomial(Fraction(Integer)))
+--E 169
+
+--S 170 of 1406
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Fraction(Polynomial(Fraction(Integer)))
+--E 170
+
+)clear all
+
+--S 171 of 1406
+t0:=(a+b*x^2)^5*(A+B*x^2)
+--R
+--R
+--R (1)
+--R 5 12 5 4 10 4 2 3 8
+--R B b x + (A b + 5B a b )x + (5A a b + 10B a b )x
+--R +
+--R 2 3 3 2 6 3 2 4 4 4 5 2 5
+--R (10A a b + 10B a b )x + (10A a b + 5B a b)x + (5A a b + B a )x + A a
+--R Type: Polynomial(Integer)
+--E 171
+
+--S 172 of 1406
+r0:=a^5*A*x+1/3*a^4*(5*A*b+a*B)*x^3+a^3*b*(2*A*b+a*B)*x^5+_
+ 10/7*a^2*b^2*(A*b+a*B)*x^7+5/9*a*b^3*(A*b+2*a*B)*x^9+_
+ 1/11*b^4*(A*b+5*a*B)*x^11+1/13*b^5*B*x^13
+--R
+--R
+--R (2)
+--R 1 5 13 1 5 5 4 11 5 4 10 2 3 9
+--R -- B b x + (-- A b + -- B a b )x + (- A a b + -- B a b )x
+--R 13 11 11 9 9
+--R +
+--R 10 2 3 10 3 2 7 3 2 4 5 5 4 1 5 3
+--R (-- A a b + -- B a b )x + (2A a b + B a b)x + (- A a b + - B a )x
+--R 7 7 3 3
+--R +
+--R 5
+--R A a x
+--R Type: Polynomial(Fraction(Integer))
+--E 172
+
+--S 173 of 1406
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 1 5 13 1 5 5 4 11 5 4 10 2 3 9
+--R -- B b x + (-- A b + -- B a b )x + (- A a b + -- B a b )x
+--R 13 11 11 9 9
+--R +
+--R 10 2 3 10 3 2 7 3 2 4 5 5 4 1 5 3
+--R (-- A a b + -- B a b )x + (2A a b + B a b)x + (- A a b + - B a )x
+--R 7 7 3 3
+--R +
+--R 5
+--R A a x
+--R Type: Polynomial(Fraction(Integer))
+--E 173
+
+--S 174 of 1406
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Polynomial(Fraction(Integer))
+--E 174
+
+--S 175 of 1406
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Polynomial(Fraction(Integer))
+--E 175
+
+)clear all
+
+--S 176 of 1406
+t0:=(a+b*x^2)^5*(A+B*x^2)/x
+--R
+--R
+--R (1)
+--R 5 12 5 4 10 4 2 3 8
+--R B b x + (A b + 5B a b )x + (5A a b + 10B a b )x
+--R +
+--R 2 3 3 2 6 3 2 4 4 4 5 2 5
+--R (10A a b + 10B a b )x + (10A a b + 5B a b)x + (5A a b + B a )x + A a
+--R /
+--R x
+--R Type: Fraction(Polynomial(Integer))
+--E 176
+
+--S 177 of 1406
+r0:=5/2*a^4*A*b*x^2+5/2*a^3*A*b^2*x^4+5/3*a^2*A*b^3*x^6+5/8*a*A*b^4*x^8+_
+ 1/10*A*b^5*x^10+1/12*B*(a+b*x^2)^6/b+a^5*A*log(x)
+--R
+--R
+--R (2)
+--R 5 6 12 6 5 10
+--R 120A a b log(x) + 10B b x + (12A b + 60B a b )x
+--R +
+--R 5 2 4 8 2 4 3 3 6
+--R (75A a b + 150B a b )x + (200A a b + 200B a b )x
+--R +
+--R 3 3 4 2 4 4 2 5 2 6
+--R (300A a b + 150B a b )x + (300A a b + 60B a b)x + 10B a
+--R /
+--R 120b
+--R Type: Expression(Integer)
+--E 177
+
+--S 178 of 1406
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 5 5 12 5 4 10
+--R 120A a log(x) + 10B b x + (12A b + 60B a b )x
+--R +
+--R 4 2 3 8 2 3 3 2 6
+--R (75A a b + 150B a b )x + (200A a b + 200B a b )x
+--R +
+--R 3 2 4 4 4 5 2
+--R (300A a b + 150B a b)x + (300A a b + 60B a )x
+--R /
+--R 120
+--R Type: Union(Expression(Integer),...)
+--E 178
+
+--S 179 of 1406
+m0:=a0-r0
+--R
+--R
+--R 6
+--R B a
+--R (4) - ----
+--R 12b
+--R Type: Expression(Integer)
+--E 179
+
+--S 180 of 1406
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 180
+
+)clear all
+
+--S 181 of 1406
+t0:=(a+b*x^2)^5*(A+B*x^2)/x^2
+--R
+--R
+--R (1)
+--R 5 12 5 4 10 4 2 3 8
+--R B b x + (A b + 5B a b )x + (5A a b + 10B a b )x
+--R +
+--R 2 3 3 2 6 3 2 4 4 4 5 2 5
+--R (10A a b + 10B a b )x + (10A a b + 5B a b)x + (5A a b + B a )x + A a
+--R /
+--R 2
+--R x
+--R Type: Fraction(Polynomial(Integer))
+--E 181
+
+--S 182 of 1406
+r0:=-a^5*A/x+a^4*(5*A*b+a*B)*x+5/3*a^3*b*(2*A*b+a*B)*x^3+_
+ 2*a^2*b^2*(A*b+a*B)*x^5+5/7*a*b^3*(A*b+2*a*B)*x^7+_
+ 1/9*b^4*(A*b+5*a*B)*x^9+1/11*b^5*B*x^11
+--R
+--R
+--R (2)
+--R 5 12 5 4 10 4 2 3 8
+--R 63B b x + (77A b + 385B a b )x + (495A a b + 990B a b )x
+--R +
+--R 2 3 3 2 6 3 2 4 4
+--R (1386A a b + 1386B a b )x + (2310A a b + 1155B a b)x
+--R +
+--R 4 5 2 5
+--R (3465A a b + 693B a )x - 693A a
+--R /
+--R 693x
+--R Type: Fraction(Polynomial(Integer))
+--E 182
+
+--S 183 of 1406
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 5 12 5 4 10 4 2 3 8
+--R 63B b x + (77A b + 385B a b )x + (495A a b + 990B a b )x
+--R +
+--R 2 3 3 2 6 3 2 4 4
+--R (1386A a b + 1386B a b )x + (2310A a b + 1155B a b)x
+--R +
+--R 4 5 2 5
+--R (3465A a b + 693B a )x - 693A a
+--R /
+--R 693x
+--R Type: Union(Expression(Integer),...)
+--E 183
+
+--S 184 of 1406
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 184
+
+--S 185 of 1406
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 185
+
+)clear all
+
+--S 186 of 1406
+t0:=(a+b*x^2)^5*(A+B*x^2)/x^3
+--R
+--R
+--R (1)
+--R 5 12 5 4 10 4 2 3 8
+--R B b x + (A b + 5B a b )x + (5A a b + 10B a b )x
+--R +
+--R 2 3 3 2 6 3 2 4 4 4 5 2 5
+--R (10A a b + 10B a b )x + (10A a b + 5B a b)x + (5A a b + B a )x + A a
+--R /
+--R 3
+--R x
+--R Type: Fraction(Polynomial(Integer))
+--E 186
+
+--S 187 of 1406
+r0:=-1/2*a^5*A/x^2+5/2*a^3*b*(2*A*b+a*B)*x^2+5/2*a^2*b^2*(A*b+a*B)*x^4+_
+ 5/6*a*b^3*(A*b+2*a*B)*x^6+1/8*b^4*(A*b+5*a*B)*x^8+1/10*b^5*B*x^10+_
+ a^4*(5*A*b+a*B)*log(x)
+--R
+--R
+--R (2)
+--R 4 5 2 5 12 5 4 10
+--R (600A a b + 120B a )x log(x) + 12B b x + (15A b + 75B a b )x
+--R +
+--R 4 2 3 8 2 3 3 2 6
+--R (100A a b + 200B a b )x + (300A a b + 300B a b )x
+--R +
+--R 3 2 4 4 5
+--R (600A a b + 300B a b)x - 60A a
+--R /
+--R 2
+--R 120x
+--R Type: Expression(Integer)
+--E 187
+
+--S 188 of 1406
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 4 5 2 5 12 5 4 10
+--R (600A a b + 120B a )x log(x) + 12B b x + (15A b + 75B a b )x
+--R +
+--R 4 2 3 8 2 3 3 2 6
+--R (100A a b + 200B a b )x + (300A a b + 300B a b )x
+--R +
+--R 3 2 4 4 5
+--R (600A a b + 300B a b)x - 60A a
+--R /
+--R 2
+--R 120x
+--R Type: Union(Expression(Integer),...)
+--E 188
+
+--S 189 of 1406
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 189
+
+--S 190 of 1406
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 190
+
+)clear all
+
+--S 191 of 1406
+t0:=(a+b*x^2)^5*(A+B*x^2)/x^4
+--R
+--R
+--R (1)
+--R 5 12 5 4 10 4 2 3 8
+--R B b x + (A b + 5B a b )x + (5A a b + 10B a b )x
+--R +
+--R 2 3 3 2 6 3 2 4 4 4 5 2 5
+--R (10A a b + 10B a b )x + (10A a b + 5B a b)x + (5A a b + B a )x + A a
+--R /
+--R 4
+--R x
+--R Type: Fraction(Polynomial(Integer))
+--E 191
+
+--S 192 of 1406
+r0:=-1/3*a^5*A/x^3-a^4*(5*A*b+a*B)/x+5*a^3*b*(2*A*b+a*B)*x+_
+ 10/3*a^2*b^2*(A*b+a*B)*x^3+a*b^3*(A*b+2*a*B)*x^5+_
+ 1/7*b^4*(A*b+5*a*B)*x^7+1/9*b^5*B*x^9
+--R
+--R
+--R (2)
+--R 1 5 12 1 5 5 4 10 4 2 3 8
+--R - B b x + (- A b + - B a b )x + (A a b + 2B a b )x
+--R 9 7 7
+--R +
+--R 10 2 3 10 3 2 6 3 2 4 4 4 5 2
+--R (-- A a b + -- B a b )x + (10A a b + 5B a b)x + (- 5A a b - B a )x
+--R 3 3
+--R +
+--R 1 5
+--R - - A a
+--R 3
+--R /
+--R 3
+--R x
+--R Type: Fraction(Polynomial(Fraction(Integer)))
+--E 192
+
+--S 193 of 1406
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 5 12 5 4 10 4 2 3 8
+--R 7B b x + (9A b + 45B a b )x + (63A a b + 126B a b )x
+--R +
+--R 2 3 3 2 6 3 2 4 4
+--R (210A a b + 210B a b )x + (630A a b + 315B a b)x
+--R +
+--R 4 5 2 5
+--R (- 315A a b - 63B a )x - 21A a
+--R /
+--R 3
+--R 63x
+--R Type: Union(Expression(Integer),...)
+--E 193
+
+--S 194 of 1406
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 194
+
+--S 195 of 1406
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 195
+
+)clear all
+
+--S 196 of 1406
+t0:=(a+b*x^2)^5*(A+B*x^2)/x^5
+--R
+--R
+--R (1)
+--R 5 12 5 4 10 4 2 3 8
+--R B b x + (A b + 5B a b )x + (5A a b + 10B a b )x
+--R +
+--R 2 3 3 2 6 3 2 4 4 4 5 2 5
+--R (10A a b + 10B a b )x + (10A a b + 5B a b)x + (5A a b + B a )x + A a
+--R /
+--R 5
+--R x
+--R Type: Fraction(Polynomial(Integer))
+--E 196
+
+--S 197 of 1406
+r0:=-1/4*a^5*A/x^4-1/2*a^4*(5*A*b+a*B)/x^2+5*a^2*b^2*(A*b+a*B)*x^2+_
+ 5/4*a*b^3*(A*b+2*a*B)*x^4+1/6*b^4*(A*b+5*a*B)*x^6+_
+ 1/8*b^5*B*x^8+5*a^3*b*(2*A*b+a*B)*log(x)
+--R
+--R
+--R (2)
+--R 3 2 4 4 5 12 5 4 10
+--R (240A a b + 120B a b)x log(x) + 3B b x + (4A b + 20B a b )x
+--R +
+--R 4 2 3 8 2 3 3 2 6
+--R (30A a b + 60B a b )x + (120A a b + 120B a b )x
+--R +
+--R 4 5 2 5
+--R (- 60A a b - 12B a )x - 6A a
+--R /
+--R 4
+--R 24x
+--R Type: Expression(Integer)
+--E 197
+
+--S 198 of 1406
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 3 2 4 4 5 12 5 4 10
+--R (240A a b + 120B a b)x log(x) + 3B b x + (4A b + 20B a b )x
+--R +
+--R 4 2 3 8 2 3 3 2 6
+--R (30A a b + 60B a b )x + (120A a b + 120B a b )x
+--R +
+--R 4 5 2 5
+--R (- 60A a b - 12B a )x - 6A a
+--R /
+--R 4
+--R 24x
+--R Type: Union(Expression(Integer),...)
+--E 198
+
+--S 199 of 1406
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 199
+
+--S 200 of 1406
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 200
+
+)clear all
+
+--S 201 of 1406
+t0:=(a+b*x^2)^5*(A+B*x^2)/x^6
+--R
+--R
+--R (1)
+--R 5 12 5 4 10 4 2 3 8
+--R B b x + (A b + 5B a b )x + (5A a b + 10B a b )x
+--R +
+--R 2 3 3 2 6 3 2 4 4 4 5 2 5
+--R (10A a b + 10B a b )x + (10A a b + 5B a b)x + (5A a b + B a )x + A a
+--R /
+--R 6
+--R x
+--R Type: Fraction(Polynomial(Integer))
+--E 201
+
+--S 202 of 1406
+r0:=-1/5*a^5*A/x^5-1/3*a^4*(5*A*b+a*B)/x^3-5*a^3*b*(2*A*b+a*B)/x+_
+ 10*a^2*b^2*(A*b+a*B)*x+5/3*a*b^3*(A*b+2*a*B)*x^3+_
+ 1/5*b^4*(A*b+5*a*B)*x^5+1/7*b^5*B*x^7
+--R
+--R
+--R (2)
+--R 1 5 12 1 5 4 10 5 4 10 2 3 8
+--R - B b x + (- A b + B a b )x + (- A a b + -- B a b )x
+--R 7 5 3 3
+--R +
+--R 2 3 3 2 6 3 2 4 4
+--R (10A a b + 10B a b )x + (- 10A a b - 5B a b)x
+--R +
+--R 5 4 1 5 2 1 5
+--R (- - A a b - - B a )x - - A a
+--R 3 3 5
+--R /
+--R 5
+--R x
+--R Type: Fraction(Polynomial(Fraction(Integer)))
+--E 202
+
+--S 203 of 1406
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 5 12 5 4 10 4 2 3 8
+--R 15B b x + (21A b + 105B a b )x + (175A a b + 350B a b )x
+--R +
+--R 2 3 3 2 6 3 2 4 4
+--R (1050A a b + 1050B a b )x + (- 1050A a b - 525B a b)x
+--R +
+--R 4 5 2 5
+--R (- 175A a b - 35B a )x - 21A a
+--R /
+--R 5
+--R 105x
+--R Type: Union(Expression(Integer),...)
+--E 203
+
+--S 204 of 1406
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 204
+
+--S 205 of 1406
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 205
+
+)clear all
+
+--S 206 of 1406
+t0:=(a+b*x^2)^5*(A+B*x^2)/x^7
+--R
+--R
+--R (1)
+--R 5 12 5 4 10 4 2 3 8
+--R B b x + (A b + 5B a b )x + (5A a b + 10B a b )x
+--R +
+--R 2 3 3 2 6 3 2 4 4 4 5 2 5
+--R (10A a b + 10B a b )x + (10A a b + 5B a b)x + (5A a b + B a )x + A a
+--R /
+--R 7
+--R x
+--R Type: Fraction(Polynomial(Integer))
+--E 206
+
+--S 207 of 1406
+r0:=-1/6*a^5*A/x^6-1/4*a^4*(5*A*b+a*B)/x^4-5/2*a^3*b*(2*A*b+a*B)/x^2+_
+ 5/2*a*b^3*(A*b+2*a*B)*x^2+1/4*b^4*(A*b+5*a*B)*x^4+1/6*b^5*B*x^6+_
+ 10*a^2*b^2*(A*b+a*B)*log(x)
+--R
+--R
+--R (2)
+--R 2 3 3 2 6 5 12 5 4 10
+--R (120A a b + 120B a b )x log(x) + 2B b x + (3A b + 15B a b )x
+--R +
+--R 4 2 3 8 3 2 4 4
+--R (30A a b + 60B a b )x + (- 60A a b - 30B a b)x
+--R +
+--R 4 5 2 5
+--R (- 15A a b - 3B a )x - 2A a
+--R /
+--R 6
+--R 12x
+--R Type: Expression(Integer)
+--E 207
+
+--S 208 of 1406
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 2 3 3 2 6 5 12 5 4 10
+--R (120A a b + 120B a b )x log(x) + 2B b x + (3A b + 15B a b )x
+--R +
+--R 4 2 3 8 3 2 4 4
+--R (30A a b + 60B a b )x + (- 60A a b - 30B a b)x
+--R +
+--R 4 5 2 5
+--R (- 15A a b - 3B a )x - 2A a
+--R /
+--R 6
+--R 12x
+--R Type: Union(Expression(Integer),...)
+--E 208
+
+--S 209 of 1406
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 209
+
+--S 210 of 1406
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 210
+
+)clear all
+
+--S 211 of 1406
+t0:=(a+b*x^2)^5*(A+B*x^2)/x^8
+--R
+--R
+--R (1)
+--R 5 12 5 4 10 4 2 3 8
+--R B b x + (A b + 5B a b )x + (5A a b + 10B a b )x
+--R +
+--R 2 3 3 2 6 3 2 4 4 4 5 2 5
+--R (10A a b + 10B a b )x + (10A a b + 5B a b)x + (5A a b + B a )x + A a
+--R /
+--R 8
+--R x
+--R Type: Fraction(Polynomial(Integer))
+--E 211
+
+--S 212 of 1406
+r0:=-1/7*a^5*A/x^7-1/5*a^4*(5*A*b+a*B)/x^5-5/3*a^3*b*(2*A*b+a*B)/x^3-_
+ 10*a^2*b^2*(A*b+a*B)/x+5*a*b^3*(A*b+2*a*B)*x+_
+ 1/3*b^4*(A*b+5*a*B)*x^3+1/5*b^5*B*x^5
+--R
+--R
+--R (2)
+--R 1 5 12 1 5 5 4 10 4 2 3 8
+--R - B b x + (- A b + - B a b )x + (5A a b + 10B a b )x
+--R 5 3 3
+--R +
+--R 2 3 3 2 6 10 3 2 5 4 4
+--R (- 10A a b - 10B a b )x + (- -- A a b - - B a b)x
+--R 3 3
+--R +
+--R 4 1 5 2 1 5
+--R (- A a b - - B a )x - - A a
+--R 5 7
+--R /
+--R 7
+--R x
+--R Type: Fraction(Polynomial(Fraction(Integer)))
+--E 212
+
+--S 213 of 1406
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 5 12 5 4 10 4 2 3 8
+--R 21B b x + (35A b + 175B a b )x + (525A a b + 1050B a b )x
+--R +
+--R 2 3 3 2 6 3 2 4 4
+--R (- 1050A a b - 1050B a b )x + (- 350A a b - 175B a b)x
+--R +
+--R 4 5 2 5
+--R (- 105A a b - 21B a )x - 15A a
+--R /
+--R 7
+--R 105x
+--R Type: Union(Expression(Integer),...)
+--E 213
+
+--S 214 of 1406
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 214
+
+--S 215 of 1406
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 215
+
+)clear all
+
+--S 216 of 1406
+t0:=(a+b*x^2)^5*(A+B*x^2)/x^9
+--R
+--R
+--R (1)
+--R 5 12 5 4 10 4 2 3 8
+--R B b x + (A b + 5B a b )x + (5A a b + 10B a b )x
+--R +
+--R 2 3 3 2 6 3 2 4 4 4 5 2 5
+--R (10A a b + 10B a b )x + (10A a b + 5B a b)x + (5A a b + B a )x + A a
+--R /
+--R 9
+--R x
+--R Type: Fraction(Polynomial(Integer))
+--E 216
+
+--S 217 of 1406
+r0:=-1/8*a^5*A/x^8-1/6*a^4*(5*A*b+a*B)/x^6-5/4*a^3*b*(2*A*b+a*B)/x^4-_
+ 5*a^2*b^2*(A*b+a*B)/x^2+1/2*b^4*(A*b+5*a*B)*x^2+1/4*b^5*B*x^4+_
+ 5*a*b^3*(A*b+2*a*B)*log(x)
+--R
+--R
+--R (2)
+--R 4 2 3 8 5 12 5 4 10
+--R (120A a b + 240B a b )x log(x) + 6B b x + (12A b + 60B a b )x
+--R +
+--R 2 3 3 2 6 3 2 4 4
+--R (- 120A a b - 120B a b )x + (- 60A a b - 30B a b)x
+--R +
+--R 4 5 2 5
+--R (- 20A a b - 4B a )x - 3A a
+--R /
+--R 8
+--R 24x
+--R Type: Expression(Integer)
+--E 217
+
+--S 218 of 1406
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 4 2 3 8 5 12 5 4 10
+--R (120A a b + 240B a b )x log(x) + 6B b x + (12A b + 60B a b )x
+--R +
+--R 2 3 3 2 6 3 2 4 4
+--R (- 120A a b - 120B a b )x + (- 60A a b - 30B a b)x
+--R +
+--R 4 5 2 5
+--R (- 20A a b - 4B a )x - 3A a
+--R /
+--R 8
+--R 24x
+--R Type: Union(Expression(Integer),...)
+--E 218
+
+--S 219 of 1406
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 219
+
+--S 220 of 1406
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 220
+
+)clear all
+
+--S 221 of 1406
+t0:=(a+b*x^2)^5*(A+B*x^2)/x^10
+--R
+--R
+--R (1)
+--R 5 12 5 4 10 4 2 3 8
+--R B b x + (A b + 5B a b )x + (5A a b + 10B a b )x
+--R +
+--R 2 3 3 2 6 3 2 4 4 4 5 2 5
+--R (10A a b + 10B a b )x + (10A a b + 5B a b)x + (5A a b + B a )x + A a
+--R /
+--R 10
+--R x
+--R Type: Fraction(Polynomial(Integer))
+--E 221
+
+--S 222 of 1406
+r0:=-1/9*a^5*A/x^9-1/7*a^4*(5*A*b+a*B)/x^7-a^3*b*(2*A*b+a*B)/x^5-_
+ 10/3*a^2*b^2*(A*b+a*B)/x^3-5*a*b^3*(A*b+2*a*B)/x+_
+ b^4*(A*b+5*a*B)*x+1/3*b^5*B*x^3
+--R
+--R
+--R (2)
+--R 1 5 12 5 4 10 4 2 3 8
+--R - B b x + (A b + 5B a b )x + (- 5A a b - 10B a b )x
+--R 3
+--R +
+--R 10 2 3 10 3 2 6 3 2 4 4
+--R (- -- A a b - -- B a b )x + (- 2A a b - B a b)x
+--R 3 3
+--R +
+--R 5 4 1 5 2 1 5
+--R (- - A a b - - B a )x - - A a
+--R 7 7 9
+--R /
+--R 9
+--R x
+--R Type: Fraction(Polynomial(Fraction(Integer)))
+--E 222
+
+--S 223 of 1406
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 5 12 5 4 10 4 2 3 8
+--R 21B b x + (63A b + 315B a b )x + (- 315A a b - 630B a b )x
+--R +
+--R 2 3 3 2 6 3 2 4 4
+--R (- 210A a b - 210B a b )x + (- 126A a b - 63B a b)x
+--R +
+--R 4 5 2 5
+--R (- 45A a b - 9B a )x - 7A a
+--R /
+--R 9
+--R 63x
+--R Type: Union(Expression(Integer),...)
+--E 223
+
+--S 224 of 1406
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 224
+
+--S 225 of 1406
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 225
+
+)clear all
+
+--S 226 of 1406
+t0:=(a+b*x^2)^5*(A+B*x^2)/x^11
+--R
+--R
+--R (1)
+--R 5 12 5 4 10 4 2 3 8
+--R B b x + (A b + 5B a b )x + (5A a b + 10B a b )x
+--R +
+--R 2 3 3 2 6 3 2 4 4 4 5 2 5
+--R (10A a b + 10B a b )x + (10A a b + 5B a b)x + (5A a b + B a )x + A a
+--R /
+--R 11
+--R x
+--R Type: Fraction(Polynomial(Integer))
+--E 226
+
+--S 227 of 1406
+r0:=-1/10*a^5*A/x^10-1/8*a^4*(5*A*b+a*B)/x^8-5/6*a^3*b*(2*A*b+a*B)/x^6-_
+ 5/2*a^2*b^2*(A*b+a*B)/x^4-5/2*a*b^3*(A*b+2*a*B)/x^2+_
+ 1/2*b^5*B*x^2+b^4*(A*b+5*a*B)*log(x)
+--R
+--R
+--R (2)
+--R 5 4 10 5 12 4 2 3 8
+--R (120A b + 600B a b )x log(x) + 60B b x + (- 300A a b - 600B a b )x
+--R +
+--R 2 3 3 2 6 3 2 4 4
+--R (- 300A a b - 300B a b )x + (- 200A a b - 100B a b)x
+--R +
+--R 4 5 2 5
+--R (- 75A a b - 15B a )x - 12A a
+--R /
+--R 10
+--R 120x
+--R Type: Expression(Integer)
+--E 227
+
+--S 228 of 1406
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 5 4 10 5 12 4 2 3 8
+--R (120A b + 600B a b )x log(x) + 60B b x + (- 300A a b - 600B a b )x
+--R +
+--R 2 3 3 2 6 3 2 4 4
+--R (- 300A a b - 300B a b )x + (- 200A a b - 100B a b)x
+--R +
+--R 4 5 2 5
+--R (- 75A a b - 15B a )x - 12A a
+--R /
+--R 10
+--R 120x
+--R Type: Union(Expression(Integer),...)
+--E 228
+
+--S 229 of 1406
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 229
+
+--S 230 of 1406
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 230
+
+)clear all
+
+--S 231 of 1406
+t0:=(a+b*x^2)^5*(A+B*x^2)/x^12
+--R
+--R
+--R (1)
+--R 5 12 5 4 10 4 2 3 8
+--R B b x + (A b + 5B a b )x + (5A a b + 10B a b )x
+--R +
+--R 2 3 3 2 6 3 2 4 4 4 5 2 5
+--R (10A a b + 10B a b )x + (10A a b + 5B a b)x + (5A a b + B a )x + A a
+--R /
+--R 12
+--R x
+--R Type: Fraction(Polynomial(Integer))
+--E 231
+
+--S 232 of 1406
+r0:=-1/11*a^5*A/x^11-1/9*a^4*(5*A*b+a*B)/x^9-5/7*a^3*b*(2*A*b+a*B)/x^7-_
+ 2*a^2*b^2*(A*b+a*B)/x^5-5/3*a*b^3*(A*b+2*a*B)/x^3-_
+ b^4*(A*b+5*a*B)/x+b^5*B*x
+--R
+--R
+--R (2)
+--R 5 12 5 4 10 5 4 10 2 3 8
+--R B b x + (- A b - 5B a b )x + (- - A a b - -- B a b )x
+--R 3 3
+--R +
+--R 2 3 3 2 6 10 3 2 5 4 4
+--R (- 2A a b - 2B a b )x + (- -- A a b - - B a b)x
+--R 7 7
+--R +
+--R 5 4 1 5 2 1 5
+--R (- - A a b - - B a )x - -- A a
+--R 9 9 11
+--R /
+--R 11
+--R x
+--R Type: Fraction(Polynomial(Fraction(Integer)))
+--E 232
+
+--S 233 of 1406
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 5 12 5 4 10 4 2 3 8
+--R 693B b x + (- 693A b - 3465B a b )x + (- 1155A a b - 2310B a b )x
+--R +
+--R 2 3 3 2 6 3 2 4 4
+--R (- 1386A a b - 1386B a b )x + (- 990A a b - 495B a b)x
+--R +
+--R 4 5 2 5
+--R (- 385A a b - 77B a )x - 63A a
+--R /
+--R 11
+--R 693x
+--R Type: Union(Expression(Integer),...)
+--E 233
+
+--S 234 of 1406
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 234
+
+--S 235 of 1406
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 235
+
+)clear all
+
+--S 236 of 1406
+t0:=(a+b*x^2)^5*(A+B*x^2)/x^13
+--R
+--R
+--R (1)
+--R 5 12 5 4 10 4 2 3 8
+--R B b x + (A b + 5B a b )x + (5A a b + 10B a b )x
+--R +
+--R 2 3 3 2 6 3 2 4 4 4 5 2 5
+--R (10A a b + 10B a b )x + (10A a b + 5B a b)x + (5A a b + B a )x + A a
+--R /
+--R 13
+--R x
+--R Type: Fraction(Polynomial(Integer))
+--E 236
+
+--S 237 of 1406
+r0:=-1/10*a^5*B/x^10-5/8*a^4*b*B/x^8-5/3*a^3*b^2*B/x^6-5/2*a^2*b^3*B/x^4-_
+ 5/2*a*b^4*B/x^2-1/12*A*(a+b*x^2)^6/(a*x^12)+b^5*B*log(x)
+--R
+--R
+--R (2)
+--R 5 12 6 12 5 2 4 10
+--R 120B a b x log(x) - 10A b x + (- 60A a b - 300B a b )x
+--R +
+--R 2 4 3 3 8 3 3 4 2 6
+--R (- 150A a b - 300B a b )x + (- 200A a b - 200B a b )x
+--R +
+--R 4 2 5 4 5 6 2 6
+--R (- 150A a b - 75B a b)x + (- 60A a b - 12B a )x - 10A a
+--R /
+--R 12
+--R 120a x
+--R Type: Expression(Integer)
+--E 237
+
+--S 238 of 1406
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 5 12 5 4 10
+--R 120B b x log(x) + (- 60A b - 300B a b )x
+--R +
+--R 4 2 3 8 2 3 3 2 6
+--R (- 150A a b - 300B a b )x + (- 200A a b - 200B a b )x
+--R +
+--R 3 2 4 4 4 5 2 5
+--R (- 150A a b - 75B a b)x + (- 60A a b - 12B a )x - 10A a
+--R /
+--R 12
+--R 120x
+--R Type: Union(Expression(Integer),...)
+--E 238
+
+--S 239 of 1406
+m0:=a0-r0
+--R
+--R
+--R 6
+--R A b
+--R (4) ----
+--R 12a
+--R Type: Expression(Integer)
+--E 239
+
+--S 240 of 1406
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 240
+
+)clear all
+
+--S 241 of 1406
+t0:=(a+b*x^2)^5*(A+B*x^2)/x^14
+--R
+--R
+--R (1)
+--R 5 12 5 4 10 4 2 3 8
+--R B b x + (A b + 5B a b )x + (5A a b + 10B a b )x
+--R +
+--R 2 3 3 2 6 3 2 4 4 4 5 2 5
+--R (10A a b + 10B a b )x + (10A a b + 5B a b)x + (5A a b + B a )x + A a
+--R /
+--R 14
+--R x
+--R Type: Fraction(Polynomial(Integer))
+--E 241
+
+--S 242 of 1406
+r0:=-1/13*a^5*A/x^13-1/11*a^4*(5*A*b+a*B)/x^11-5/9*a^3*b*_
+ (2*A*b+a*B)/x^9-10/7*a^2*b^2*(A*b+a*B)/x^7-a*b^3*_
+ (A*b+2*a*B)/x^5-1/3*b^4*(A*b+5*a*B)/x^3-b^5*B/x
+--R
+--R
+--R (2)
+--R 5 12 1 5 5 4 10 4 2 3 8
+--R - B b x + (- - A b - - B a b )x + (- A a b - 2B a b )x
+--R 3 3
+--R +
+--R 10 2 3 10 3 2 6 10 3 2 5 4 4
+--R (- -- A a b - -- B a b )x + (- -- A a b - - B a b)x
+--R 7 7 9 9
+--R +
+--R 5 4 1 5 2 1 5
+--R (- -- A a b - -- B a )x - -- A a
+--R 11 11 13
+--R /
+--R 13
+--R x
+--R Type: Fraction(Polynomial(Fraction(Integer)))
+--E 242
+
+--S 243 of 1406
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 5 12 5 4 10
+--R - 9009B b x + (- 3003A b - 15015B a b )x
+--R +
+--R 4 2 3 8 2 3 3 2 6
+--R (- 9009A a b - 18018B a b )x + (- 12870A a b - 12870B a b )x
+--R +
+--R 3 2 4 4 4 5 2 5
+--R (- 10010A a b - 5005B a b)x + (- 4095A a b - 819B a )x - 693A a
+--R /
+--R 13
+--R 9009x
+--R Type: Union(Expression(Integer),...)
+--E 243
+
+--S 244 of 1406
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 244
+
+--S 245 of 1406
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 245
+
+)clear all
+
+--S 246 of 1406
+t0:=(a+b*x^2)^5*(A+B*x^2)/x^15
+--R
+--R
+--R (1)
+--R 5 12 5 4 10 4 2 3 8
+--R B b x + (A b + 5B a b )x + (5A a b + 10B a b )x
+--R +
+--R 2 3 3 2 6 3 2 4 4 4 5 2 5
+--R (10A a b + 10B a b )x + (10A a b + 5B a b)x + (5A a b + B a )x + A a
+--R /
+--R 15
+--R x
+--R Type: Fraction(Polynomial(Integer))
+--E 246
+
+--S 247 of 1406
+r0:=-1/14*A*(a+b*x^2)^6/(a*x^14)+1/84*(A*b-7*a*B)*(a+b*x^2)^6/(a^2*x^12)
+--R
+--R
+--R (2)
+--R 1 7 1 6 14 1 2 5 12 1 2 5 5 3 4 10
+--R (-- A b - -- B a b )x - - B a b x + (- - A a b - - B a b )x
+--R 84 12 2 4 4
+--R +
+--R 5 3 4 5 4 3 8 5 4 3 5 5 2 6
+--R (- - A a b - - B a b )x + (- - A a b - - B a b )x
+--R 6 3 4 4
+--R +
+--R 5 2 1 6 4 5 6 1 7 2 1 7
+--R (- A a b - - B a b)x + (- -- A a b - -- B a )x - -- A a
+--R 2 12 12 14
+--R /
+--R 2 14
+--R a x
+--R Type: Fraction(Polynomial(Fraction(Integer)))
+--E 247
+
+--S 248 of 1406
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 5 12 5 4 10 4 2 3 8
+--R - 42B b x + (- 21A b - 105B a b )x + (- 70A a b - 140B a b )x
+--R +
+--R 2 3 3 2 6 3 2 4 4
+--R (- 105A a b - 105B a b )x + (- 84A a b - 42B a b)x
+--R +
+--R 4 5 2 5
+--R (- 35A a b - 7B a )x - 6A a
+--R /
+--R 14
+--R 84x
+--R Type: Union(Expression(Integer),...)
+--E 248
+
+--S 249 of 1406
+m0:=a0-r0
+--R
+--R
+--R 7 6
+--R - A b + 7B a b
+--R (4) ----------------
+--R 2
+--R 84a
+--R Type: Expression(Integer)
+--E 249
+
+--S 250 of 1406
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 250
+
+)clear all
+
+--S 251 of 1406
+t0:=(a+b*x^2)^5*(A+B*x^2)/x^16
+--R
+--R
+--R (1)
+--R 5 12 5 4 10 4 2 3 8
+--R B b x + (A b + 5B a b )x + (5A a b + 10B a b )x
+--R +
+--R 2 3 3 2 6 3 2 4 4 4 5 2 5
+--R (10A a b + 10B a b )x + (10A a b + 5B a b)x + (5A a b + B a )x + A a
+--R /
+--R 16
+--R x
+--R Type: Fraction(Polynomial(Integer))
+--E 251
+
+--S 252 of 1406
+r0:=-1/15*a^5*A/x^15-1/13*a^4*(5*A*b+a*B)/x^13-5/11*a^3*b*(2*A*b+a*B)/_
+ x^11-10/9*a^2*b^2*(A*b+a*B)/x^9-5/7*a*b^3*(A*b+2*a*B)/x^7-_
+ 1/5*b^4*(A*b+5*a*B)/x^5-1/3*b^5*B/x^3
+--R
+--R
+--R (2)
+--R 1 5 12 1 5 4 10 5 4 10 2 3 8
+--R - - B b x + (- - A b - B a b )x + (- - A a b - -- B a b )x
+--R 3 5 7 7
+--R +
+--R 10 2 3 10 3 2 6 10 3 2 5 4 4
+--R (- -- A a b - -- B a b )x + (- -- A a b - -- B a b)x
+--R 9 9 11 11
+--R +
+--R 5 4 1 5 2 1 5
+--R (- -- A a b - -- B a )x - -- A a
+--R 13 13 15
+--R /
+--R 15
+--R x
+--R Type: Fraction(Polynomial(Fraction(Integer)))
+--E 252
+
+--S 253 of 1406
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 5 12 5 4 10
+--R - 15015B b x + (- 9009A b - 45045B a b )x
+--R +
+--R 4 2 3 8 2 3 3 2 6
+--R (- 32175A a b - 64350B a b )x + (- 50050A a b - 50050B a b )x
+--R +
+--R 3 2 4 4 4 5 2 5
+--R (- 40950A a b - 20475B a b)x + (- 17325A a b - 3465B a )x - 3003A a
+--R /
+--R 15
+--R 45045x
+--R Type: Union(Expression(Integer),...)
+--E 253
+
+--S 254 of 1406
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 254
+
+--S 255 of 1406
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 255
+
+)clear all
+
+--S 256 of 1406
+t0:=(a+b*x^2)^5*(A+B*x^2)/x^17
+--R
+--R
+--R (1)
+--R 5 12 5 4 10 4 2 3 8
+--R B b x + (A b + 5B a b )x + (5A a b + 10B a b )x
+--R +
+--R 2 3 3 2 6 3 2 4 4 4 5 2 5
+--R (10A a b + 10B a b )x + (10A a b + 5B a b)x + (5A a b + B a )x + A a
+--R /
+--R 17
+--R x
+--R Type: Fraction(Polynomial(Integer))
+--E 256
+
+--S 257 of 1406
+r0:=-1/16*A*(a+b*x^2)^6/(a*x^16)+1/56*(A*b-4*a*B)*(a+b*x^2)^6/_
+ (a^2*x^14)-1/336*b*(A*b-4*a*B)*(a+b*x^2)^6/(a^3*x^12)
+--R
+--R
+--R (2)
+--R 1 8 1 7 16 1 3 5 12 1 3 5 5 4 4 10
+--R (- --- A b + -- B a b )x - - B a b x + (- - A a b - - B a b )x
+--R 336 84 4 6 6
+--R +
+--R 5 4 4 5 5 3 8 5 3 6 2 6
+--R (- - A a b - - B a b )x + (- A a b - B a b )x
+--R 8 4
+--R +
+--R 5 6 2 5 7 4 5 7 1 8 2 1 8
+--R (- - A a b - -- B a b)x + (- -- A a b - -- B a )x - -- A a
+--R 6 12 14 14 16
+--R /
+--R 3 16
+--R a x
+--R Type: Fraction(Polynomial(Fraction(Integer)))
+--E 257
+
+--S 258 of 1406
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 5 12 5 4 10 4 2 3 8
+--R - 84B b x + (- 56A b - 280B a b )x + (- 210A a b - 420B a b )x
+--R +
+--R 2 3 3 2 6 3 2 4 4
+--R (- 336A a b - 336B a b )x + (- 280A a b - 140B a b)x
+--R +
+--R 4 5 2 5
+--R (- 120A a b - 24B a )x - 21A a
+--R /
+--R 16
+--R 336x
+--R Type: Union(Expression(Integer),...)
+--E 258
+
+--S 259 of 1406
+m0:=a0-r0
+--R
+--R
+--R 8 7
+--R A b - 4B a b
+--R (4) --------------
+--R 3
+--R 336a
+--R Type: Expression(Integer)
+--E 259
+
+--S 260 of 1406
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 260
+
+)clear all
+
+--S 261 of 1406
+t0:=(a+b*x^2)^5*(A+B*x^2)/x^18
+--R
+--R
+--R (1)
+--R 5 12 5 4 10 4 2 3 8
+--R B b x + (A b + 5B a b )x + (5A a b + 10B a b )x
+--R +
+--R 2 3 3 2 6 3 2 4 4 4 5 2 5
+--R (10A a b + 10B a b )x + (10A a b + 5B a b)x + (5A a b + B a )x + A a
+--R /
+--R 18
+--R x
+--R Type: Fraction(Polynomial(Integer))
+--E 261
+
+--S 262 of 1406
+r0:=-1/17*a^5*A/x^17-1/15*a^4*(5*A*b+a*B)/x^15-5/13*a^3*b*_
+ (2*A*b+a*B)/x^13-10/11*a^2*b^2*(A*b+a*B)/x^11-_
+ 5/9*a*b^3*(A*b+2*a*B)/x^9-1/7*b^4*(A*b+5*a*B)/x^7-1/5*b^5*B/x^5
+--R
+--R
+--R (2)
+--R 1 5 12 1 5 5 4 10 5 4 10 2 3 8
+--R - - B b x + (- - A b - - B a b )x + (- - A a b - -- B a b )x
+--R 5 7 7 9 9
+--R +
+--R 10 2 3 10 3 2 6 10 3 2 5 4 4
+--R (- -- A a b - -- B a b )x + (- -- A a b - -- B a b)x
+--R 11 11 13 13
+--R +
+--R 1 4 1 5 2 1 5
+--R (- - A a b - -- B a )x - -- A a
+--R 3 15 17
+--R /
+--R 17
+--R x
+--R Type: Fraction(Polynomial(Fraction(Integer)))
+--E 262
+
+--S 263 of 1406
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 5 12 5 4 10
+--R - 153153B b x + (- 109395A b - 546975B a b )x
+--R +
+--R 4 2 3 8 2 3 3 2 6
+--R (- 425425A a b - 850850B a b )x + (- 696150A a b - 696150B a b )x
+--R +
+--R 3 2 4 4 4 5 2
+--R (- 589050A a b - 294525B a b)x + (- 255255A a b - 51051B a )x
+--R +
+--R 5
+--R - 45045A a
+--R /
+--R 17
+--R 765765x
+--R Type: Union(Expression(Integer),...)
+--E 263
+
+--S 264 of 1406
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 264
+
+--S 265 of 1406
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 265
+
+)clear all
+
+--S 266 of 1406
+t0:=(a+b*x^2)^5*(A+B*x^2)/x^19
+--R
+--R
+--R (1)
+--R 5 12 5 4 10 4 2 3 8
+--R B b x + (A b + 5B a b )x + (5A a b + 10B a b )x
+--R +
+--R 2 3 3 2 6 3 2 4 4 4 5 2 5
+--R (10A a b + 10B a b )x + (10A a b + 5B a b)x + (5A a b + B a )x + A a
+--R /
+--R 19
+--R x
+--R Type: Fraction(Polynomial(Integer))
+--E 266
+
+--S 267 of 1406
+r0:=-1/18*a^5*A/x^18-1/16*a^4*(5*A*b+a*B)/x^16-5/14*a^3*b*_
+ (2*A*b+a*B)/x^14-5/6*a^2*b^2*(A*b+a*B)/x^12-1/2*a*b^3*_
+ (A*b+2*a*B)/x^10-1/8*b^4*(A*b+5*a*B)/x^8-1/6*b^5*B/x^6
+--R
+--R
+--R (2)
+--R 1 5 12 1 5 5 4 10 1 4 2 3 8
+--R - - B b x + (- - A b - - B a b )x + (- - A a b - B a b )x
+--R 6 8 8 2
+--R +
+--R 5 2 3 5 3 2 6 5 3 2 5 4 4
+--R (- - A a b - - B a b )x + (- - A a b - -- B a b)x
+--R 6 6 7 14
+--R +
+--R 5 4 1 5 2 1 5
+--R (- -- A a b - -- B a )x - -- A a
+--R 16 16 18
+--R /
+--R 18
+--R x
+--R Type: Fraction(Polynomial(Fraction(Integer)))
+--E 267
+
+--S 268 of 1406
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 5 12 5 4 10 4 2 3 8
+--R - 168B b x + (- 126A b - 630B a b )x + (- 504A a b - 1008B a b )x
+--R +
+--R 2 3 3 2 6 3 2 4 4
+--R (- 840A a b - 840B a b )x + (- 720A a b - 360B a b)x
+--R +
+--R 4 5 2 5
+--R (- 315A a b - 63B a )x - 56A a
+--R /
+--R 18
+--R 1008x
+--R Type: Union(Expression(Integer),...)
+--E 268
+
+--S 269 of 1406
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 269
+
+--S 270 of 1406
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 270
+
+)clear all
+
+--S 271 of 1406
+t0:=(a+b*x^2)^5*(A+B*x^2)/x^20
+--R
+--R
+--R (1)
+--R 5 12 5 4 10 4 2 3 8
+--R B b x + (A b + 5B a b )x + (5A a b + 10B a b )x
+--R +
+--R 2 3 3 2 6 3 2 4 4 4 5 2 5
+--R (10A a b + 10B a b )x + (10A a b + 5B a b)x + (5A a b + B a )x + A a
+--R /
+--R 20
+--R x
+--R Type: Fraction(Polynomial(Integer))
+--E 271
+
+--S 272 of 1406
+r0:=-1/19*a^5*A/x^19-1/17*a^4*(5*A*b+a*B)/x^17-1/3*a^3*b*_
+ (2*A*b+a*B)/x^15-10/13*a^2*b^2*(A*b+a*B)/x^13-5/11*a*b^3*_
+ (A*b+2*a*B)/x^11-1/9*b^4*(A*b+5*a*B)/x^9-1/7*b^5*B/x^7
+--R
+--R
+--R (2)
+--R 1 5 12 1 5 5 4 10 5 4 10 2 3 8
+--R - - B b x + (- - A b - - B a b )x + (- -- A a b - -- B a b )x
+--R 7 9 9 11 11
+--R +
+--R 10 2 3 10 3 2 6 2 3 2 1 4 4
+--R (- -- A a b - -- B a b )x + (- - A a b - - B a b)x
+--R 13 13 3 3
+--R +
+--R 5 4 1 5 2 1 5
+--R (- -- A a b - -- B a )x - -- A a
+--R 17 17 19
+--R /
+--R 19
+--R x
+--R Type: Fraction(Polynomial(Fraction(Integer)))
+--E 272
+
+--S 273 of 1406
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 5 12 5 4 10
+--R - 415701B b x + (- 323323A b - 1616615B a b )x
+--R +
+--R 4 2 3 8 2 3 3 2 6
+--R (- 1322685A a b - 2645370B a b )x + (- 2238390A a b - 2238390B a b )x
+--R +
+--R 3 2 4 4 4 5 2
+--R (- 1939938A a b - 969969B a b)x + (- 855855A a b - 171171B a )x
+--R +
+--R 5
+--R - 153153A a
+--R /
+--R 19
+--R 2909907x
+--R Type: Union(Expression(Integer),...)
+--E 273
+
+--S 274 of 1406
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 274
+
+--S 275 of 1406
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 275
+
+)clear all
+
+--S 276 of 1406
+t0:=(a+b*x^2)^5*(A+B*x^2)/x^21
+--R
+--R
+--R (1)
+--R 5 12 5 4 10 4 2 3 8
+--R B b x + (A b + 5B a b )x + (5A a b + 10B a b )x
+--R +
+--R 2 3 3 2 6 3 2 4 4 4 5 2 5
+--R (10A a b + 10B a b )x + (10A a b + 5B a b)x + (5A a b + B a )x + A a
+--R /
+--R 21
+--R x
+--R Type: Fraction(Polynomial(Integer))
+--E 276
+
+--S 277 of 1406
+r0:=-1/20*a^5*A/x^20-1/18*a^4*(5*A*b+a*B)/x^18-5/16*a^3*b*_
+ (2*A*b+a*B)/x^16-5/7*a^2*b^2*(A*b+a*B)/x^14-5/12*a*b^3*_
+ (A*b+2*a*B)/x^12-1/10*b^4*(A*b+5*a*B)/x^10-1/8*b^5*B/x^8
+--R
+--R
+--R (2)
+--R 1 5 12 1 5 1 4 10 5 4 5 2 3 8
+--R - - B b x + (- -- A b - - B a b )x + (- -- A a b - - B a b )x
+--R 8 10 2 12 6
+--R +
+--R 5 2 3 5 3 2 6 5 3 2 5 4 4
+--R (- - A a b - - B a b )x + (- - A a b - -- B a b)x
+--R 7 7 8 16
+--R +
+--R 5 4 1 5 2 1 5
+--R (- -- A a b - -- B a )x - -- A a
+--R 18 18 20
+--R /
+--R 20
+--R x
+--R Type: Fraction(Polynomial(Fraction(Integer)))
+--E 277
+
+--S 278 of 1406
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 5 12 5 4 10
+--R - 630B b x + (- 504A b - 2520B a b )x
+--R +
+--R 4 2 3 8 2 3 3 2 6
+--R (- 2100A a b - 4200B a b )x + (- 3600A a b - 3600B a b )x
+--R +
+--R 3 2 4 4 4 5 2 5
+--R (- 3150A a b - 1575B a b)x + (- 1400A a b - 280B a )x - 252A a
+--R /
+--R 20
+--R 5040x
+--R Type: Union(Expression(Integer),...)
+--E 278
+
+--S 279 of 1406
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 279
+
+--S 280 of 1406
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 280
+
+)clear all
+
+--S 281 of 1406
+t0:=(a+b*x^2)^5*(A+B*x^2)/x^22
+--R
+--R
+--R (1)
+--R 5 12 5 4 10 4 2 3 8
+--R B b x + (A b + 5B a b )x + (5A a b + 10B a b )x
+--R +
+--R 2 3 3 2 6 3 2 4 4 4 5 2 5
+--R (10A a b + 10B a b )x + (10A a b + 5B a b)x + (5A a b + B a )x + A a
+--R /
+--R 22
+--R x
+--R Type: Fraction(Polynomial(Integer))
+--E 281
+
+--S 282 of 1406
+r0:=-1/21*a^5*A/x^21-1/19*a^4*(5*A*b+a*B)/x^19-5/17*a^3*b*_
+ (2*A*b+a*B)/x^17-2/3*a^2*b^2*(A*b+a*B)/x^15-5/13*a*b^3*_
+ (A*b+2*a*B)/x^13-1/11*b^4*(A*b+5*a*B)/x^11-1/9*b^5*B/x^9
+--R
+--R
+--R (2)
+--R 1 5 12 1 5 5 4 10 5 4 10 2 3 8
+--R - - B b x + (- -- A b - -- B a b )x + (- -- A a b - -- B a b )x
+--R 9 11 11 13 13
+--R +
+--R 2 2 3 2 3 2 6 10 3 2 5 4 4
+--R (- - A a b - - B a b )x + (- -- A a b - -- B a b)x
+--R 3 3 17 17
+--R +
+--R 5 4 1 5 2 1 5
+--R (- -- A a b - -- B a )x - -- A a
+--R 19 19 21
+--R /
+--R 21
+--R x
+--R Type: Fraction(Polynomial(Fraction(Integer)))
+--E 282
+
+--S 283 of 1406
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 5 12 5 4 10
+--R - 323323B b x + (- 264537A b - 1322685B a b )x
+--R +
+--R 4 2 3 8 2 3 3 2 6
+--R (- 1119195A a b - 2238390B a b )x + (- 1939938A a b - 1939938B a b )x
+--R +
+--R 3 2 4 4 4 5 2
+--R (- 1711710A a b - 855855B a b)x + (- 765765A a b - 153153B a )x
+--R +
+--R 5
+--R - 138567A a
+--R /
+--R 21
+--R 2909907x
+--R Type: Union(Expression(Integer),...)
+--E 283
+
+--S 284 of 1406
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 284
+
+--S 285 of 1406
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 285
+
+)clear all
+
+--S 286 of 1406
+t0:=(a+b*x^2)^5*(A+B*x^2)/x^23
+--R
+--R
+--R (1)
+--R 5 12 5 4 10 4 2 3 8
+--R B b x + (A b + 5B a b )x + (5A a b + 10B a b )x
+--R +
+--R 2 3 3 2 6 3 2 4 4 4 5 2 5
+--R (10A a b + 10B a b )x + (10A a b + 5B a b)x + (5A a b + B a )x + A a
+--R /
+--R 23
+--R x
+--R Type: Fraction(Polynomial(Integer))
+--E 286
+
+--S 287 of 1406
+r0:=-1/22*a^5*A/x^22-1/20*a^4*(5*A*b+a*B)/x^20-5/18*a^3*b*_
+ (2*A*b+a*B)/x^18-5/8*a^2*b^2*(A*b+a*B)/x^16-5/14*a*b^3*_
+ (A*b+2*a*B)/x^14-1/12*b^4*(A*b+5*a*B)/x^12-1/10*b^5*B/x^10
+--R
+--R
+--R (2)
+--R 1 5 12 1 5 5 4 10 5 4 5 2 3 8
+--R - -- B b x + (- -- A b - -- B a b )x + (- -- A a b - - B a b )x
+--R 10 12 12 14 7
+--R +
+--R 5 2 3 5 3 2 6 5 3 2 5 4 4
+--R (- - A a b - - B a b )x + (- - A a b - -- B a b)x
+--R 8 8 9 18
+--R +
+--R 1 4 1 5 2 1 5
+--R (- - A a b - -- B a )x - -- A a
+--R 4 20 22
+--R /
+--R 22
+--R x
+--R Type: Fraction(Polynomial(Fraction(Integer)))
+--E 287
+
+--S 288 of 1406
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 5 12 5 4 10
+--R - 2772B b x + (- 2310A b - 11550B a b )x
+--R +
+--R 4 2 3 8 2 3 3 2 6
+--R (- 9900A a b - 19800B a b )x + (- 17325A a b - 17325B a b )x
+--R +
+--R 3 2 4 4 4 5 2 5
+--R (- 15400A a b - 7700B a b)x + (- 6930A a b - 1386B a )x - 1260A a
+--R /
+--R 22
+--R 27720x
+--R Type: Union(Expression(Integer),...)
+--E 288
+
+--S 289 of 1406
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 289
+
+--S 290 of 1406
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 290
+
+)clear all
+
+--S 291 of 1406
+t0:=x^6*(A+B*x^2)/(a+b*x^2)
+--R
+--R
+--R 8 6
+--R B x + A x
+--R (1) -----------
+--R 2
+--R b x + a
+--R Type: Fraction(Polynomial(Integer))
+--E 291
+
+--S 292 of 1406
+r0:=a^2*(A*b-a*B)*x/b^4-1/3*a*(A*b-a*B)*x^3/b^3+1/5*(A*b-a*B)*x^5/b^2+_
+ 1/7*B*x^7/b-a^(5/2)*(A*b-a*B)*atan(x*sqrt(b)/sqrt(a))/b^(9/2)
+--R
+--R
+--R (2)
+--R +-+
+--R 2 3 +-+ x\|b
+--R (- 105A a b + 105B a )\|a atan(-----)
+--R +-+
+--R \|a
+--R +
+--R 3 7 3 2 5 2 2 3
+--R 15B b x + (21A b - 21B a b )x + (- 35A a b + 35B a b)x
+--R +
+--R 2 3
+--R (105A a b - 105B a )x
+--R *
+--R +-+
+--R \|b
+--R /
+--R 4 +-+
+--R 105b \|b
+--R Type: Expression(Integer)
+--E 292
+
+--S 293 of 1406
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R +---+
+--R | a 2
+--R +---+ - 2b x |- - + b x - a
+--R 2 3 | a \| b 3 7
+--R (105A a b - 105B a ) |- - log(-----------------------) + 30B b x
+--R \| b 2
+--R b x + a
+--R +
+--R 3 2 5 2 2 3 2 3
+--R (42A b - 42B a b )x + (- 70A a b + 70B a b)x + (210A a b - 210B a )x
+--R /
+--R 4
+--R 210b
+--R ,
+--R
+--R +-+
+--R |a
+--R +-+ |-
+--R 2 3 |a \|b 3 7 3 2 5
+--R (105A a b - 105B a ) |- atan(----) + 15B b x + (21A b - 21B a b )x
+--R \|b x
+--R +
+--R 2 2 3 2 3
+--R (- 35A a b + 35B a b)x + (105A a b - 105B a )x
+--R /
+--R 4
+--R 105b
+--R ]
+--R Type: Union(List(Expression(Integer)),...)
+--E 293
+
+--S 294 of 1406
+m0a:=a0.1-r0
+--R
+--R
+--R (4)
+--R +---+
+--R | a 2
+--R +---+ - 2b x |- - + b x - a
+--R 2 3 | a +-+ \| b
+--R (A a b - B a ) |- - \|b log(-----------------------)
+--R \| b 2
+--R b x + a
+--R +
+--R +-+
+--R 2 3 +-+ x\|b
+--R (2A a b - 2B a )\|a atan(-----)
+--R +-+
+--R \|a
+--R /
+--R 4 +-+
+--R 2b \|b
+--R Type: Expression(Integer)
+--E 294
+
+--S 295 of 1406
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 295
+
+--S 296 of 1406
+m0b:=a0.2-r0
+--R
+--R
+--R +-+
+--R |a
+--R +-+ +-+ |-
+--R 2 3 +-+ x\|b 2 3 |a +-+ \|b
+--R (A a b - B a )\|a atan(-----) + (A a b - B a ) |- \|b atan(----)
+--R +-+ \|b x
+--R \|a
+--R (6) ----------------------------------------------------------------
+--R 4 +-+
+--R b \|b
+--R Type: Expression(Integer)
+--E 296
+
+--S 297 of 1406
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 297
+
+)clear all
+
+--S 298 of 1406
+t0:=x^5*(A+B*x^2)/(a+b*x^2)
+--R
+--R
+--R 7 5
+--R B x + A x
+--R (1) -----------
+--R 2
+--R b x + a
+--R Type: Fraction(Polynomial(Integer))
+--E 298
+
+--S 299 of 1406
+r0:=-1/2*a*(A*b-a*B)*x^2/b^3+1/4*(A*b-a*B)*x^4/b^2+1/6*B*x^6/b+_
+ 1/2*a^2*(A*b-a*B)*log(a+b*x^2)/b^4
+--R
+--R
+--R (2)
+--R 2 3 2 3 6 3 2 4
+--R (6A a b - 6B a )log(b x + a) + 2B b x + (3A b - 3B a b )x
+--R +
+--R 2 2 2
+--R (- 6A a b + 6B a b)x
+--R /
+--R 4
+--R 12b
+--R Type: Expression(Integer)
+--E 299
+
+--S 300 of 1406
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 2 3 2 3 6 3 2 4
+--R (6A a b - 6B a )log(b x + a) + 2B b x + (3A b - 3B a b )x
+--R +
+--R 2 2 2
+--R (- 6A a b + 6B a b)x
+--R /
+--R 4
+--R 12b
+--R Type: Union(Expression(Integer),...)
+--E 300
+
+--S 301 of 1406
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 301
+
+--S 302 of 1406
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 302
+
+)clear all
+
+--S 303 of 1406
+t0:=x^4*(A+B*x^2)/(a+b*x^2)
+--R
+--R
+--R 6 4
+--R B x + A x
+--R (1) -----------
+--R 2
+--R b x + a
+--R Type: Fraction(Polynomial(Integer))
+--E 303
+
+--S 304 of 1406
+r0:=-a*(A*b-a*B)*x/b^3+1/3*(A*b-a*B)*x^3/b^2+1/5*B*x^5/b+_
+ a^(3/2)*(A*b-a*B)*atan(x*sqrt(b)/sqrt(a))/b^(7/2)
+--R
+--R
+--R (2)
+--R +-+
+--R 2 +-+ x\|b
+--R (15A a b - 15B a )\|a atan(-----)
+--R +-+
+--R \|a
+--R +
+--R 2 5 2 3 2 +-+
+--R (3B b x + (5A b - 5B a b)x + (- 15A a b + 15B a )x)\|b
+--R /
+--R 3 +-+
+--R 15b \|b
+--R Type: Expression(Integer)
+--E 304
+
+--S 305 of 1406
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R +---+
+--R | a 2
+--R +---+ 2b x |- - + b x - a
+--R 2 | a \| b 2 5
+--R (15A a b - 15B a ) |- - log(---------------------) + 6B b x
+--R \| b 2
+--R b x + a
+--R +
+--R 2 3 2
+--R (10A b - 10B a b)x + (- 30A a b + 30B a )x
+--R /
+--R 3
+--R 30b
+--R ,
+--R
+--R +-+
+--R |a
+--R +-+ |-
+--R 2 |a \|b 2 5 2 3
+--R (- 15A a b + 15B a ) |- atan(----) + 3B b x + (5A b - 5B a b)x
+--R \|b x
+--R +
+--R 2
+--R (- 15A a b + 15B a )x
+--R /
+--R 3
+--R 15b
+--R ]
+--R Type: Union(List(Expression(Integer)),...)
+--E 305
+
+--S 306 of 1406
+m0a:=a0.1-r0
+--R
+--R
+--R (4)
+--R +---+
+--R | a 2
+--R +---+ 2b x |- - + b x - a
+--R 2 | a +-+ \| b
+--R (A a b - B a ) |- - \|b log(---------------------)
+--R \| b 2
+--R b x + a
+--R +
+--R +-+
+--R 2 +-+ x\|b
+--R (- 2A a b + 2B a )\|a atan(-----)
+--R +-+
+--R \|a
+--R /
+--R 3 +-+
+--R 2b \|b
+--R Type: Expression(Integer)
+--E 306
+
+--S 307 of 1406
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 307
+
+--S 308 of 1406
+m0b:=a0.2-r0
+--R
+--R
+--R +-+
+--R |a
+--R +-+ +-+ |-
+--R 2 +-+ x\|b 2 |a +-+ \|b
+--R (- A a b + B a )\|a atan(-----) + (- A a b + B a ) |- \|b atan(----)
+--R +-+ \|b x
+--R \|a
+--R (6) --------------------------------------------------------------------
+--R 3 +-+
+--R b \|b
+--R Type: Expression(Integer)
+--E 308
+
+--S 309 of 1406
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 309
+
+)clear all
+
+--S 310 of 1406
+t0:=x^3*(A+B*x^2)/(a+b*x^2)
+--R
+--R
+--R 5 3
+--R B x + A x
+--R (1) -----------
+--R 2
+--R b x + a
+--R Type: Fraction(Polynomial(Integer))
+--E 310
+
+--S 311 of 1406
+r0:=1/2*(A*b-a*B)*x^2/b^2+1/4*B*x^4/b-1/2*a*(A*b-a*B)*log(a+b*x^2)/b^3
+--R
+--R
+--R 2 2 2 4 2 2
+--R (- 2A a b + 2B a )log(b x + a) + B b x + (2A b - 2B a b)x
+--R (2) -------------------------------------------------------------
+--R 3
+--R 4b
+--R Type: Expression(Integer)
+--E 311
+
+--S 312 of 1406
+a0:=integrate(t0,x)
+--R
+--R
+--R 2 2 2 4 2 2
+--R (- 2A a b + 2B a )log(b x + a) + B b x + (2A b - 2B a b)x
+--R (3) -------------------------------------------------------------
+--R 3
+--R 4b
+--R Type: Union(Expression(Integer),...)
+--E 312
+
+--S 313 of 1406
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 313
+
+--S 314 of 1406
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 314
+
+)clear all
+
+--S 315 of 1406
+t0:=x^2*(A+B*x^2)/(a+b*x^2)
+--R
+--R
+--R 4 2
+--R B x + A x
+--R (1) -----------
+--R 2
+--R b x + a
+--R Type: Fraction(Polynomial(Integer))
+--E 315
+
+--S 316 of 1406
+r0:=(A*b-a*B)*x/b^2+1/3*B*x^3/b-(A*b-a*B)*atan(x*sqrt(b)/sqrt(a))*_
+ sqrt(a)/b^(5/2)
+--R
+--R
+--R +-+
+--R +-+ x\|b 3 +-+
+--R (- 3A b + 3B a)\|a atan(-----) + (B b x + (3A b - 3B a)x)\|b
+--R +-+
+--R \|a
+--R (2) --------------------------------------------------------------
+--R 2 +-+
+--R 3b \|b
+--R Type: Expression(Integer)
+--E 316
+
+--S 317 of 1406
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +---+
+--R | a 2
+--R +---+ - 2b x |- - + b x - a
+--R | a \| b 3
+--R (3A b - 3B a) |- - log(-----------------------) + 2B b x + (6A b - 6B a)x
+--R \| b 2
+--R b x + a
+--R [--------------------------------------------------------------------------,
+--R 2
+--R 6b
+--R +-+
+--R |a
+--R +-+ |-
+--R |a \|b 3
+--R (3A b - 3B a) |- atan(----) + B b x + (3A b - 3B a)x
+--R \|b x
+--R -----------------------------------------------------]
+--R 2
+--R 3b
+--R Type: Union(List(Expression(Integer)),...)
+--E 317
+
+--S 318 of 1406
+m0a:=a0.1-r0
+--R
+--R
+--R (4)
+--R +---+
+--R | a 2
+--R +---+ - 2b x |- - + b x - a
+--R | a +-+ \| b
+--R (A b - B a) |- - \|b log(-----------------------)
+--R \| b 2
+--R b x + a
+--R +
+--R +-+
+--R +-+ x\|b
+--R (2A b - 2B a)\|a atan(-----)
+--R +-+
+--R \|a
+--R /
+--R 2 +-+
+--R 2b \|b
+--R Type: Expression(Integer)
+--E 318
+
+--S 319 of 1406
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 319
+
+--S 320 of 1406
+m0b:=a0.2-r0
+--R
+--R
+--R +-+
+--R |a
+--R +-+ +-+ |-
+--R +-+ x\|b |a +-+ \|b
+--R (A b - B a)\|a atan(-----) + (A b - B a) |- \|b atan(----)
+--R +-+ \|b x
+--R \|a
+--R (6) ----------------------------------------------------------
+--R 2 +-+
+--R b \|b
+--R Type: Expression(Integer)
+--E 320
+
+--S 321 of 1406
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 321
+
+)clear all
+
+--S 322 of 1406
+t0:=x*(A+B*x^2)/(a+b*x^2)
+--R
+--R
+--R 3
+--R B x + A x
+--R (1) ----------
+--R 2
+--R b x + a
+--R Type: Fraction(Polynomial(Integer))
+--E 322
+
+--S 323 of 1406
+r0:=1/2*B*x^2/b+1/2*(A*b-a*B)*log(a+b*x^2)/b^2
+--R
+--R
+--R 2 2
+--R (A b - B a)log(b x + a) + B b x
+--R (2) ---------------------------------
+--R 2
+--R 2b
+--R Type: Expression(Integer)
+--E 323
+
+--S 324 of 1406
+a0:=integrate(t0,x)
+--R
+--R
+--R 2 2
+--R (A b - B a)log(b x + a) + B b x
+--R (3) ---------------------------------
+--R 2
+--R 2b
+--R Type: Union(Expression(Integer),...)
+--E 324
+
+--S 325 of 1406
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 325
+
+--S 326 of 1406
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 326
+
+)clear all
+
+--S 327 of 1406
+t0:=(A+B*x^2)/(a+b*x^2)
+--R
+--R
+--R 2
+--R B x + A
+--R (1) --------
+--R 2
+--R b x + a
+--R Type: Fraction(Polynomial(Integer))
+--E 327
+
+--S 328 of 1406
+r0:=B*x/b+(A*b-a*B)*atan(x*sqrt(b)/sqrt(a))/(b^(3/2)*sqrt(a))
+--R
+--R
+--R +-+
+--R x\|b +-+ +-+
+--R (A b - B a)atan(-----) + B x\|a \|b
+--R +-+
+--R \|a
+--R (2) ------------------------------------
+--R +-+ +-+
+--R b\|a \|b
+--R Type: Expression(Integer)
+--E 328
+
+--S 329 of 1406
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 2 +-----+
+--R (b x - a)\|- a b + 2a b x +-----+
+--R (A b - B a)log(---------------------------) + 2B x\|- a b
+--R 2
+--R b x + a
+--R [----------------------------------------------------------,
+--R +-----+
+--R 2b\|- a b
+--R +---+
+--R x\|a b +---+
+--R (A b - B a)atan(-------) + B x\|a b
+--R a
+--R ------------------------------------]
+--R +---+
+--R b\|a b
+--R Type: Union(List(Expression(Integer)),...)
+--E 329
+
+--S 330 of 1406
+m0a:=a0.1-r0
+--R
+--R
+--R (4)
+--R 2 +-----+
+--R +-+ +-+ (b x - a)\|- a b + 2a b x
+--R (A b - B a)\|a \|b log(---------------------------)
+--R 2
+--R b x + a
+--R +
+--R +-+
+--R +-----+ x\|b
+--R (- 2A b + 2B a)\|- a b atan(-----)
+--R +-+
+--R \|a
+--R /
+--R +-----+ +-+ +-+
+--R 2b\|- a b \|a \|b
+--R Type: Expression(Integer)
+--E 330
+
+--S 331 of 1406
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 331
+
+--S 332 of 1406
+m0b:=a0.2-r0
+--R
+--R
+--R +---+ +-+
+--R +-+ +-+ x\|a b +---+ x\|b
+--R (A b - B a)\|a \|b atan(-------) + (- A b + B a)\|a b atan(-----)
+--R a +-+
+--R \|a
+--R (6) -----------------------------------------------------------------
+--R +-+ +-+ +---+
+--R b\|a \|b \|a b
+--R Type: Expression(Integer)
+--E 332
+
+--S 333 of 1406
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 333
+
+)clear all
+
+--S 334 of 1406
+t0:=(A+B*x^2)/(a-b*x^2)
+--R
+--R
+--R 2
+--R - B x - A
+--R (1) ----------
+--R 2
+--R b x - a
+--R Type: Fraction(Polynomial(Integer))
+--E 334
+
+--S 335 of 1406
+r0:=-B*x/b+(A*b+a*B)*atanh(x*sqrt(b)/sqrt(a))/(b^(3/2)*sqrt(a))
+--R
+--R
+--R +-+
+--R x\|b +-+ +-+
+--R (A b + B a)atanh(-----) - B x\|a \|b
+--R +-+
+--R \|a
+--R (2) -------------------------------------
+--R +-+ +-+
+--R b\|a \|b
+--R Type: Expression(Integer)
+--E 335
+
+--S 336 of 1406
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 2 +---+
+--R (b x + a)\|a b + 2a b x +---+
+--R (A b + B a)log(-------------------------) - 2B x\|a b
+--R 2
+--R b x - a
+--R [------------------------------------------------------,
+--R +---+
+--R 2b\|a b
+--R +-----+
+--R x\|- a b +-----+
+--R (A b + B a)atan(---------) - B x\|- a b
+--R a
+--R ----------------------------------------]
+--R +-----+
+--R b\|- a b
+--R Type: Union(List(Expression(Integer)),...)
+--E 336
+
+--S 337 of 1406
+m0a:=a0.1-r0
+--R
+--R
+--R (4)
+--R 2 +---+
+--R +-+ +-+ (b x + a)\|a b + 2a b x
+--R (A b + B a)\|a \|b log(-------------------------)
+--R 2
+--R b x - a
+--R +
+--R +-+
+--R +---+ x\|b
+--R (- 2A b - 2B a)\|a b atanh(-----)
+--R +-+
+--R \|a
+--R /
+--R +-+ +-+ +---+
+--R 2b\|a \|b \|a b
+--R Type: Expression(Integer)
+--E 337
+
+--S 338 of 1406
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 338
+
+--S 339 of 1406
+m0b:=a0.2-r0
+--R
+--R
+--R +-+ +-----+
+--R +-----+ x\|b +-+ +-+ x\|- a b
+--R (- A b - B a)\|- a b atanh(-----) + (A b + B a)\|a \|b atan(---------)
+--R +-+ a
+--R \|a
+--R (6) ----------------------------------------------------------------------
+--R +-----+ +-+ +-+
+--R b\|- a b \|a \|b
+--R Type: Expression(Integer)
+--E 339
+
+--S 340 of 1406
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 340
+
+)clear all
+
+--S 341 of 1406
+t0:=(A+B*x^2)/(x*(a+b*x^2))
+--R
+--R
+--R 2
+--R B x + A
+--R (1) ----------
+--R 3
+--R b x + a x
+--R Type: Fraction(Polynomial(Integer))
+--E 341
+
+--S 342 of 1406
+r0:=A*log(x)/a-1/2*(A*b-a*B)*log(a+b*x^2)/(a*b)
+--R
+--R
+--R 2
+--R (- A b + B a)log(b x + a) + 2A b log(x)
+--R (2) ----------------------------------------
+--R 2a b
+--R Type: Expression(Integer)
+--E 342
+
+--S 343 of 1406
+a0:=integrate(t0,x)
+--R
+--R
+--R 2
+--R (- A b + B a)log(b x + a) + 2A b log(x)
+--R (3) ----------------------------------------
+--R 2a b
+--R Type: Union(Expression(Integer),...)
+--E 343
+
+--S 344 of 1406
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 344
+
+--S 345 of 1406
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 345
+
+)clear all
+
+--S 346 of 1406
+t0:=(A+B*x^2)/(x^2*(a+b*x^2))
+--R
+--R
+--R 2
+--R B x + A
+--R (1) -----------
+--R 4 2
+--R b x + a x
+--R Type: Fraction(Polynomial(Integer))
+--E 346
+
+--S 347 of 1406
+r0:=-A/(a*x)-(A*b-a*B)*atan(x*sqrt(b)/sqrt(a))/(a^(3/2)*sqrt(b))
+--R
+--R
+--R +-+
+--R x\|b +-+ +-+
+--R (- A b + B a)x atan(-----) - A\|a \|b
+--R +-+
+--R \|a
+--R (2) --------------------------------------
+--R +-+ +-+
+--R a x\|a \|b
+--R Type: Expression(Integer)
+--E 347
+
+--S 348 of 1406
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 2 +-----+
+--R (b x - a)\|- a b - 2a b x +-----+
+--R (A b - B a)x log(---------------------------) - 2A\|- a b
+--R 2
+--R b x + a
+--R [----------------------------------------------------------,
+--R +-----+
+--R 2a x\|- a b
+--R +---+
+--R x\|a b +---+
+--R (- A b + B a)x atan(-------) - A\|a b
+--R a
+--R --------------------------------------]
+--R +---+
+--R a x\|a b
+--R Type: Union(List(Expression(Integer)),...)
+--E 348
+
+--S 349 of 1406
+m0a:=a0.1-r0
+--R
+--R
+--R (4)
+--R 2 +-----+
+--R +-+ +-+ (b x - a)\|- a b - 2a b x
+--R (A b - B a)\|a \|b log(---------------------------)
+--R 2
+--R b x + a
+--R +
+--R +-+
+--R +-----+ x\|b
+--R (2A b - 2B a)\|- a b atan(-----)
+--R +-+
+--R \|a
+--R /
+--R +-----+ +-+ +-+
+--R 2a\|- a b \|a \|b
+--R Type: Expression(Integer)
+--E 349
+
+--S 350 of 1406
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 350
+
+--S 351 of 1406
+m0b:=a0.2-r0
+--R
+--R
+--R +---+ +-+
+--R +-+ +-+ x\|a b +---+ x\|b
+--R (- A b + B a)\|a \|b atan(-------) + (A b - B a)\|a b atan(-----)
+--R a +-+
+--R \|a
+--R (6) -----------------------------------------------------------------
+--R +-+ +-+ +---+
+--R a\|a \|b \|a b
+--R Type: Expression(Integer)
+--E 351
+
+--S 352 of 1406
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 352
+
+)clear all
+
+--S 353 of 1406
+t0:=(A+B*x^2)/(x^3*(a+b*x^2))
+--R
+--R
+--R 2
+--R B x + A
+--R (1) -----------
+--R 5 3
+--R b x + a x
+--R Type: Fraction(Polynomial(Integer))
+--E 353
+
+--S 354 of 1406
+r0:=-1/2*A/(a*x^2)-(A*b-a*B)*log(x)/a^2+1/2*(A*b-a*B)*log(a+b*x^2)/a^2
+--R
+--R
+--R 2 2 2
+--R (A b - B a)x log(b x + a) + (- 2A b + 2B a)x log(x) - A a
+--R (2) ----------------------------------------------------------
+--R 2 2
+--R 2a x
+--R Type: Expression(Integer)
+--E 354
+
+--S 355 of 1406
+a0:=integrate(t0,x)
+--R
+--R
+--R 2 2 2
+--R (A b - B a)x log(b x + a) + (- 2A b + 2B a)x log(x) - A a
+--R (3) ----------------------------------------------------------
+--R 2 2
+--R 2a x
+--R Type: Union(Expression(Integer),...)
+--E 355
+
+--S 356 of 1406
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 356
+
+--S 357 of 1406
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 357
+
+)clear all
+
+--S 358 of 1406
+t0:=(A+B*x^2)/(x^4*(a+b*x^2))
+--R
+--R
+--R 2
+--R B x + A
+--R (1) -----------
+--R 6 4
+--R b x + a x
+--R Type: Fraction(Polynomial(Integer))
+--E 358
+
+--S 359 of 1406
+r0:=-1/3*A/(a*x^3)+(A*b-a*B)/(a^2*x)+(A*b-a*B)*atan(x*sqrt(b)/sqrt(a))*_
+ sqrt(b)/a^(5/2)
+--R
+--R
+--R +-+
+--R 3 +-+ x\|b 2 +-+
+--R (3A b - 3B a)x \|b atan(-----) + ((3A b - 3B a)x - A a)\|a
+--R +-+
+--R \|a
+--R (2) ------------------------------------------------------------
+--R 2 3 +-+
+--R 3a x \|a
+--R Type: Expression(Integer)
+--E 359
+
+--S 360 of 1406
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R +---+
+--R | b 2
+--R +---+ 2a x |- - + b x - a
+--R 3 | b \| a 2
+--R (3A b - 3B a)x |- - log(---------------------) + (6A b - 6B a)x - 2A a
+--R \| a 2
+--R b x + a
+--R [------------------------------------------------------------------------,
+--R 2 3
+--R 6a x
+--R +-+
+--R |b
+--R +-+ a |-
+--R 3 |b \|a 2
+--R (- 3A b + 3B a)x |- atan(-----) + (3A b - 3B a)x - A a
+--R \|a b x
+--R --------------------------------------------------------]
+--R 2 3
+--R 3a x
+--R Type: Union(List(Expression(Integer)),...)
+--E 360
+
+--S 361 of 1406
+m0a:=a0.1-r0
+--R
+--R
+--R (4)
+--R +---+
+--R | b 2
+--R +---+ 2a x |- - + b x - a
+--R | b +-+ \| a
+--R (A b - B a) |- - \|a log(---------------------)
+--R \| a 2
+--R b x + a
+--R +
+--R +-+
+--R +-+ x\|b
+--R (- 2A b + 2B a)\|b atan(-----)
+--R +-+
+--R \|a
+--R /
+--R 2 +-+
+--R 2a \|a
+--R Type: Expression(Integer)
+--E 361
+
+--S 362 of 1406
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 362
+
+--S 363 of 1406
+m0b:=a0.2-r0
+--R
+--R
+--R +-+
+--R |b
+--R +-+ +-+ a |-
+--R +-+ x\|b +-+ |b \|a
+--R (- A b + B a)\|b atan(-----) + (- A b + B a)\|a |- atan(-----)
+--R +-+ \|a b x
+--R \|a
+--R (6) ---------------------------------------------------------------
+--R 2 +-+
+--R a \|a
+--R Type: Expression(Integer)
+--E 363
+
+--S 364 of 1406
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 364
+
+)clear all
+
+--S 365 of 1406
+t0:=(A+B*x^2)/(x^5*(a+b*x^2))
+--R
+--R
+--R 2
+--R B x + A
+--R (1) -----------
+--R 7 5
+--R b x + a x
+--R Type: Fraction(Polynomial(Integer))
+--E 365
+
+--S 366 of 1406
+r0:=-1/4*A/(a*x^4)+1/2*(A*b-a*B)/(a^2*x^2)+b*(A*b-a*B)*log(x)/a^3-_
+ 1/2*b*(A*b-a*B)*log(a+b*x^2)/a^3
+--R
+--R
+--R (2)
+--R 2 4 2 2 4
+--R (- 2A b + 2B a b)x log(b x + a) + (4A b - 4B a b)x log(x)
+--R +
+--R 2 2 2
+--R (2A a b - 2B a )x - A a
+--R /
+--R 3 4
+--R 4a x
+--R Type: Expression(Integer)
+--E 366
+
+--S 367 of 1406
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 2 4 2 2 4
+--R (- 2A b + 2B a b)x log(b x + a) + (4A b - 4B a b)x log(x)
+--R +
+--R 2 2 2
+--R (2A a b - 2B a )x - A a
+--R /
+--R 3 4
+--R 4a x
+--R Type: Union(Expression(Integer),...)
+--E 367
+
+--S 368 of 1406
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 368
+
+--S 369 of 1406
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 369
+
+)clear all
+
+--S 370 of 1406
+t0:=(A+B*x^2)/(x^6*(a+b*x^2))
+--R
+--R
+--R 2
+--R B x + A
+--R (1) -----------
+--R 8 6
+--R b x + a x
+--R Type: Fraction(Polynomial(Integer))
+--E 370
+
+--S 371 of 1406
+r0:=-1/5*A/(a*x^5)+1/3*(A*b-a*B)/(a^2*x^3)-b*(A*b-a*B)/(a^3*x)-_
+ b^(3/2)*(A*b-a*B)*atan(x*sqrt(b)/sqrt(a))/a^(7/2)
+--R
+--R
+--R (2)
+--R +-+
+--R 2 5 +-+ x\|b
+--R (- 15A b + 15B a b)x \|b atan(-----)
+--R +-+
+--R \|a
+--R +
+--R 2 4 2 2 2 +-+
+--R ((- 15A b + 15B a b)x + (5A a b - 5B a )x - 3A a )\|a
+--R /
+--R 3 5 +-+
+--R 15a x \|a
+--R Type: Expression(Integer)
+--E 371
+
+--S 372 of 1406
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R +---+
+--R | b 2
+--R +---+ - 2a x |- - + b x - a
+--R 2 5 | b \| a
+--R (15A b - 15B a b)x |- - log(-----------------------)
+--R \| a 2
+--R b x + a
+--R +
+--R 2 4 2 2 2
+--R (- 30A b + 30B a b)x + (10A a b - 10B a )x - 6A a
+--R /
+--R 3 5
+--R 30a x
+--R ,
+--R
+--R +-+
+--R |b
+--R +-+ a |-
+--R 2 5 |b \|a 2 4
+--R (15A b - 15B a b)x |- atan(-----) + (- 15A b + 15B a b)x
+--R \|a b x
+--R +
+--R 2 2 2
+--R (5A a b - 5B a )x - 3A a
+--R /
+--R 3 5
+--R 15a x
+--R ]
+--R Type: Union(List(Expression(Integer)),...)
+--E 372
+
+--S 373 of 1406
+m0a:=a0.1-r0
+--R
+--R
+--R (4)
+--R +---+
+--R | b 2
+--R +---+ - 2a x |- - + b x - a
+--R 2 | b +-+ \| a
+--R (A b - B a b) |- - \|a log(-----------------------)
+--R \| a 2
+--R b x + a
+--R +
+--R +-+
+--R 2 +-+ x\|b
+--R (2A b - 2B a b)\|b atan(-----)
+--R +-+
+--R \|a
+--R /
+--R 3 +-+
+--R 2a \|a
+--R Type: Expression(Integer)
+--E 373
+
+--S 374 of 1406
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 374
+
+--S 375 of 1406
+m0b:=a0.2-r0
+--R
+--R
+--R +-+
+--R |b
+--R +-+ +-+ a |-
+--R 2 +-+ x\|b 2 +-+ |b \|a
+--R (A b - B a b)\|b atan(-----) + (A b - B a b)\|a |- atan(-----)
+--R +-+ \|a b x
+--R \|a
+--R (6) -----------------------------------------------------------------
+--R 3 +-+
+--R a \|a
+--R Type: Expression(Integer)
+--E 375
+
+--S 376 of 1406
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 376
+
+)clear all
+
+--S 377 of 1406
+t0:=(A+B*x^2)/(x^7*(a+b*x^2))
+--R
+--R
+--R 2
+--R B x + A
+--R (1) -----------
+--R 9 7
+--R b x + a x
+--R Type: Fraction(Polynomial(Integer))
+--E 377
+
+--S 378 of 1406
+r0:=-1/6*A/(a*x^6)+1/4*(A*b-a*B)/(a^2*x^4)-1/2*b*(A*b-a*B)/(a^3*x^2)-_
+ b^2*(A*b-a*B)*log(x)/a^4+1/2*b^2*(A*b-a*B)*log(a+b*x^2)/a^4
+--R
+--R
+--R (2)
+--R 3 2 6 2 3 2 6
+--R (6A b - 6B a b )x log(b x + a) + (- 12A b + 12B a b )x log(x)
+--R +
+--R 2 2 4 2 3 2 3
+--R (- 6A a b + 6B a b)x + (3A a b - 3B a )x - 2A a
+--R /
+--R 4 6
+--R 12a x
+--R Type: Expression(Integer)
+--E 378
+
+--S 379 of 1406
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 3 2 6 2 3 2 6
+--R (6A b - 6B a b )x log(b x + a) + (- 12A b + 12B a b )x log(x)
+--R +
+--R 2 2 4 2 3 2 3
+--R (- 6A a b + 6B a b)x + (3A a b - 3B a )x - 2A a
+--R /
+--R 4 6
+--R 12a x
+--R Type: Union(Expression(Integer),...)
+--E 379
+
+--S 380 of 1406
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 380
+
+--S 381 of 1406
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 381
+
+)clear all
+
+--S 382 of 1406
+t0:=(A+B*x^2)/(x^8*(a+b*x^2))
+--R
+--R
+--R 2
+--R B x + A
+--R (1) ------------
+--R 10 8
+--R b x + a x
+--R Type: Fraction(Polynomial(Integer))
+--E 382
+
+--S 383 of 1406
+r0:=-1/7*A/(a*x^7)+1/5*(A*b-a*B)/(a^2*x^5)-1/3*b*(A*b-a*B)/(a^3*x^3)+_
+ b^2*(A*b-a*B)/(a^4*x)+b^(5/2)*(A*b-a*B)*atan(x*sqrt(b)/sqrt(a))/a^(9/2)
+--R
+--R
+--R (2)
+--R +-+
+--R 3 2 7 +-+ x\|b
+--R (105A b - 105B a b )x \|b atan(-----)
+--R +-+
+--R \|a
+--R +
+--R 3 2 6 2 2 4
+--R (105A b - 105B a b )x + (- 35A a b + 35B a b)x
+--R +
+--R 2 3 2 3
+--R (21A a b - 21B a )x - 15A a
+--R *
+--R +-+
+--R \|a
+--R /
+--R 4 7 +-+
+--R 105a x \|a
+--R Type: Expression(Integer)
+--E 383
+
+--S 384 of 1406
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R +---+
+--R | b 2
+--R +---+ 2a x |- - + b x - a
+--R 3 2 7 | b \| a
+--R (105A b - 105B a b )x |- - log(---------------------)
+--R \| a 2
+--R b x + a
+--R +
+--R 3 2 6 2 2 4
+--R (210A b - 210B a b )x + (- 70A a b + 70B a b)x
+--R +
+--R 2 3 2 3
+--R (42A a b - 42B a )x - 30A a
+--R /
+--R 4 7
+--R 210a x
+--R ,
+--R
+--R +-+
+--R |b
+--R +-+ a |-
+--R 3 2 7 |b \|a 3 2 6
+--R (- 105A b + 105B a b )x |- atan(-----) + (105A b - 105B a b )x
+--R \|a b x
+--R +
+--R 2 2 4 2 3 2 3
+--R (- 35A a b + 35B a b)x + (21A a b - 21B a )x - 15A a
+--R /
+--R 4 7
+--R 105a x
+--R ]
+--R Type: Union(List(Expression(Integer)),...)
+--E 384
+
+--S 385 of 1406
+m0a:=a0.1-r0
+--R
+--R
+--R (4)
+--R +---+
+--R | b 2
+--R +---+ 2a x |- - + b x - a
+--R 3 2 | b +-+ \| a
+--R (A b - B a b ) |- - \|a log(---------------------)
+--R \| a 2
+--R b x + a
+--R +
+--R +-+
+--R 3 2 +-+ x\|b
+--R (- 2A b + 2B a b )\|b atan(-----)
+--R +-+
+--R \|a
+--R /
+--R 4 +-+
+--R 2a \|a
+--R Type: Expression(Integer)
+--E 385
+
+--S 386 of 1406
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 386
+
+--S 387 of 1406
+m0b:=a0.2-r0
+--R
+--R
+--R (6)
+--R +-+
+--R |b
+--R +-+ +-+ a |-
+--R 3 2 +-+ x\|b 3 2 +-+ |b \|a
+--R (- A b + B a b )\|b atan(-----) + (- A b + B a b )\|a |- atan(-----)
+--R +-+ \|a b x
+--R \|a
+--R -----------------------------------------------------------------------
+--R 4 +-+
+--R a \|a
+--R Type: Expression(Integer)
+--E 387
+
+--S 388 of 1406
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 388
+
+)clear all
+
+--S 389 of 1406
+t0:=x^9*(A+B*x^2)/(a+b*x^2)^2
+--R
+--R
+--R 11 9
+--R B x + A x
+--R (1) -------------------
+--R 2 4 2 2
+--R b x + 2a b x + a
+--R Type: Fraction(Polynomial(Integer))
+--E 389
+
+--S 390 of 1406
+r0:=1/2*a^2*(3*A*b-4*a*B)*x^2/b^5-1/4*a*(2*A*b-3*a*B)*x^4/b^4+_
+ 1/6*(A*b-2*a*B)*x^6/b^3+1/8*B*x^8/b^2-1/2*a^4*(A*b-a*B)/_
+ (b^6*(a+b*x^2))-1/2*a^3*(4*A*b-5*a*B)*log(a+b*x^2)/b^6
+--R
+--R
+--R (2)
+--R 3 2 4 2 4 5 2 5 10
+--R ((- 48A a b + 60B a b)x - 48A a b + 60B a )log(b x + a) + 3B b x
+--R +
+--R 5 4 8 4 2 3 6 2 3 3 2 4
+--R (4A b - 5B a b )x + (- 8A a b + 10B a b )x + (24A a b - 30B a b )x
+--R +
+--R 3 2 4 2 4 5
+--R (36A a b - 48B a b)x - 12A a b + 12B a
+--R /
+--R 7 2 6
+--R 24b x + 24a b
+--R Type: Expression(Integer)
+--E 390
+
+--S 391 of 1406
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 3 2 4 2 4 5 2 5 10
+--R ((- 48A a b + 60B a b)x - 48A a b + 60B a )log(b x + a) + 3B b x
+--R +
+--R 5 4 8 4 2 3 6 2 3 3 2 4
+--R (4A b - 5B a b )x + (- 8A a b + 10B a b )x + (24A a b - 30B a b )x
+--R +
+--R 3 2 4 2 4 5
+--R (36A a b - 48B a b)x - 12A a b + 12B a
+--R /
+--R 7 2 6
+--R 24b x + 24a b
+--R Type: Union(Expression(Integer),...)
+--E 391
+
+--S 392 of 1406
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 392
+
+--S 393 of 1406
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 393
+
+)clear all
+
+--S 394 of 1406
+t0:=x^8*(A+B*x^2)/(a+b*x^2)^2
+--R
+--R
+--R 10 8
+--R B x + A x
+--R (1) -------------------
+--R 2 4 2 2
+--R b x + 2a b x + a
+--R Type: Fraction(Polynomial(Integer))
+--E 394
+
+--S 395 of 1406
+r0:=1/2*a^2*(7*A*b-9*a*B)*x/b^5-1/6*a*(7*A*b-9*a*B)*x^3/b^4+_
+ 1/10*(7*A*b-9*a*B)*x^5/b^3-1/14*(7*A*b-9*a*B)*x^7/(a*b^2)+_
+ 1/2*(A*b-a*B)*x^9/(a*b*(a+b*x^2))-1/2*a^(5/2)*(7*A*b-9*a*B)*_
+ atan(x*sqrt(b)/sqrt(a))/b^(11/2)
+--R
+--R
+--R (2)
+--R +-+
+--R 2 2 3 2 3 4 +-+ x\|b
+--R ((- 735A a b + 945B a b)x - 735A a b + 945B a )\|a atan(-----)
+--R +-+
+--R \|a
+--R +
+--R 4 9 4 3 7 3 2 2 5
+--R 30B b x + (42A b - 54B a b )x + (- 98A a b + 126B a b )x
+--R +
+--R 2 2 3 3 3 4
+--R (490A a b - 630B a b)x + (735A a b - 945B a )x
+--R *
+--R +-+
+--R \|b
+--R /
+--R 6 2 5 +-+
+--R (210b x + 210a b )\|b
+--R Type: Expression(Integer)
+--E 395
+
+--S 396 of 1406
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R +---+
+--R 2 2 3 2 3 4 | a
+--R ((735A a b - 945B a b)x + 735A a b - 945B a ) |- -
+--R \| b
+--R *
+--R +---+
+--R | a 2
+--R - 2b x |- - + b x - a
+--R \| b
+--R log(-----------------------)
+--R 2
+--R b x + a
+--R +
+--R 4 9 4 3 7 3 2 2 5
+--R 60B b x + (84A b - 108B a b )x + (- 196A a b + 252B a b )x
+--R +
+--R 2 2 3 3 3 4
+--R (980A a b - 1260B a b)x + (1470A a b - 1890B a )x
+--R /
+--R 6 2 5
+--R 420b x + 420a b
+--R ,
+--R
+--R +-+
+--R |a
+--R +-+ |-
+--R 2 2 3 2 3 4 |a \|b
+--R ((735A a b - 945B a b)x + 735A a b - 945B a ) |- atan(----)
+--R \|b x
+--R +
+--R 4 9 4 3 7 3 2 2 5
+--R 30B b x + (42A b - 54B a b )x + (- 98A a b + 126B a b )x
+--R +
+--R 2 2 3 3 3 4
+--R (490A a b - 630B a b)x + (735A a b - 945B a )x
+--R /
+--R 6 2 5
+--R 210b x + 210a b
+--R ]
+--R Type: Union(List(Expression(Integer)),...)
+--E 396
+
+--S 397 of 1406
+m0a:=a0.1-r0
+--R
+--R
+--R (4)
+--R +---+
+--R | a 2
+--R +---+ - 2b x |- - + b x - a
+--R 2 3 | a +-+ \| b
+--R (7A a b - 9B a ) |- - \|b log(-----------------------)
+--R \| b 2
+--R b x + a
+--R +
+--R +-+
+--R 2 3 +-+ x\|b
+--R (14A a b - 18B a )\|a atan(-----)
+--R +-+
+--R \|a
+--R /
+--R 5 +-+
+--R 4b \|b
+--R Type: Expression(Integer)
+--E 397
+
+--S 398 of 1406
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 398
+
+--S 399 of 1406
+m0b:=a0.2-r0
+--R
+--R
+--R +-+
+--R |a
+--R +-+ +-+ |-
+--R 2 3 +-+ x\|b 2 3 |a +-+ \|b
+--R (7A a b - 9B a )\|a atan(-----) + (7A a b - 9B a ) |- \|b atan(----)
+--R +-+ \|b x
+--R \|a
+--R (6) --------------------------------------------------------------------
+--R 5 +-+
+--R 2b \|b
+--R Type: Expression(Integer)
+--E 399
+
+--S 400 of 1406
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 400
+
+)clear all
+
+--S 401 of 1406
+t0:=x^7*(A+B*x^2)/(a+b*x^2)^2
+--R
+--R
+--R 9 7
+--R B x + A x
+--R (1) -------------------
+--R 2 4 2 2
+--R b x + 2a b x + a
+--R Type: Fraction(Polynomial(Integer))
+--E 401
+
+--S 402 of 1406
+r0:=-1/2*a*(2*A*b-3*a*B)*x^2/b^4+1/4*(A*b-2*a*B)*x^4/b^3+1/6*B*x^6/b^2+_
+ 1/2*a^3*(A*b-a*B)/(b^5*(a+b*x^2))+1/2*a^2*(3*A*b-4*a*B)*log(a+b*x^2)/b^5
+--R
+--R
+--R (2)
+--R 2 2 3 2 3 4 2 4 8
+--R ((18A a b - 24B a b)x + 18A a b - 24B a )log(b x + a) + 2B b x
+--R +
+--R 4 3 6 3 2 2 4 2 2 3 2
+--R (3A b - 4B a b )x + (- 9A a b + 12B a b )x + (- 12A a b + 18B a b)x
+--R +
+--R 3 4
+--R 6A a b - 6B a
+--R /
+--R 6 2 5
+--R 12b x + 12a b
+--R Type: Expression(Integer)
+--E 402
+
+--S 403 of 1406
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 2 2 3 2 3 4 2 4 8
+--R ((18A a b - 24B a b)x + 18A a b - 24B a )log(b x + a) + 2B b x
+--R +
+--R 4 3 6 3 2 2 4 2 2 3 2
+--R (3A b - 4B a b )x + (- 9A a b + 12B a b )x + (- 12A a b + 18B a b)x
+--R +
+--R 3 4
+--R 6A a b - 6B a
+--R /
+--R 6 2 5
+--R 12b x + 12a b
+--R Type: Union(Expression(Integer),...)
+--E 403
+
+--S 404 of 1406
+m0:=a0-r0
+--R
+--R
+--R (4) 0
+--R Type: Expression(Integer)
+--E 404
+
+--S 405 of 1406
+d0:=D(m0,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 405
+
+)clear all
+
+--S 406 of 1406
+t0:=x^6*(A+B*x^2)/(a+b*x^2)^2
+--R
+--R
+--R 8 6
+--R B x + A x
+--R (1) -------------------
+--R 2 4 2 2
+--R b x + 2a b x + a
+--R Type: Fraction(Polynomial(Integer))
+--E 406
+
+--S 407 of 1406
+r0:=-1/2*a*(5*A*b-7*a*B)*x/b^4+1/6*(5*A*b-7*a*B)*x^3/b^3-_
+ 1/10*(5*A*b-7*a*B)*x^5/(a*b^2)+1/2*(A*b-a*B)*x^7/(a*b*(a+b*x^2))+_
+ 1/2*a^(3/2)*(5*A*b-7*a*B)*atan(x*sqrt(b)/sqrt(a))/b^(9/2)
+--R
+--R
+--R (2)
+--R +-+
+--R 2 2 2 2 3 +-+ x\|b
+--R ((75A a b - 105B a b)x + 75A a b - 105B a )\|a atan(-----)
+--R +-+
+--R \|a
+--R +
+--R 3 7 3 2 5 2 2 3
+--R 6B b x + (10A b - 14B a b )x + (- 50A a b + 70B a b)x
+--R +
+--R 2 3
+--R (- 75A a b + 105B a )x
+--R *
+--R +-+
+--R \|b
+--R /
+--R 5 2 4 +-+
+--R (30b x + 30a b )\|b
+--R Type: Expression(Integer)
+--E 407
+
+--S 408 of 1406
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R [
+--R +---+
+--R 2 2 2 2 3 | a
+--R ((75A a b - 105B a b)x + 75A a b - 105B a ) |- -
+--R \| b
+--R *
+--R +---+
+--R | a 2
+--R 2b x |- - + b x - a
+--R \| b
+--R log(---------------------)
+--R 2
+--R b x + a
+--R +
+--R 3 7 3 2 5 2 2 3
+--R 12B b x + (20A b - 28B a b )x + (- 100A a b + 140B a b)x
+--R +
+--R 2 3
+--R (- 150A a b + 210B a )x
+--R /
+--R 5 2 4
+--R 60b x + 60a b
+--R ,
+--R
+--R +-+
+--R |a
+--R +-+ |-
+--R 2 2 2 2 3 |a \|b 3 7
+--R ((- 75A a b + 105B a b)x - 75A a b + 105B a ) |- atan(----) + 6B b x
+--R \|b x
+--R +
+--R 3 2 5 2 2 3 2 3
+--R (10A b - 14B a b )x + (- 50A a b + 70B a b)x + (- 75A a b + 105B a )x
+--R /
+--R 5 2 4
+--R 30b x + 30a b
+--R ]
+--R Type: Union(List(Expression(Integer)),...)
+--E 408
+
+--S 409 of 1406
+m0a:=a0.1-r0
+--R
+--R
+--R (4)
+--R +---+
+--R | a 2
+--R +---+ 2b x |- - + b x - a
+--R 2 | a +-+ \| b
+--R (5A a b - 7B a ) |- - \|b log(---------------------)
+--R \| b 2
+--R b x + a
+--R +
+--R +-+
+--R 2 +-+ x\|b
+--R (- 10A a b + 14B a )\|a atan(-----)
+--R +-+
+--R \|a
+--R /
+--R 4 +-+
+--R 4b \|b
+--R Type: Expression(Integer)
+--E 409
+
+--S 410 of 1406
+d0a:=D(m0a,x)
+--R
+--R
+--R (5) 0
+--R Type: Expression(Integer)
+--E 410
+
+--S 411 of 1406
+m0b:=a0.2-r0
+--R
+--R
+--R (6)
+--R +-+
+--R |a
+--R +-+ +-+ |-
+--R 2 +-+ x\|b 2 |a +-+ \|b
+--R (- 5A a b + 7B a )\|a atan(-----) + (- 5A a b + 7B a ) |- \|b atan(----)
+--R +-+ \|b x
+--R \|a
+--R ------------------------------------------------------------------------
+--R 4 +-+
+--R 2b \|b
+--R Type: Expression(Integer)
+--E 411
+
+--S 412 of 1406
+d0b:=D(m0b,x)
+--R
+--R
+--R (7) 0
+--R Type: Expression(Integer)
+--E 412
+
+)clear all
+
+--S 413 of 1406
+t0:=x^5*(A+B*x^2)/(a+b*x^2)^2
+--R
+--R
+--R 7 5
+--R B x + A x
+--R (1) -------------------
+--R 2 4 2 2
+--R b x + 2a b x + a
+--R Type: Fraction(Polynomial(Integer))
+--E 413
+
+--S 414 of 1406
+r0:=1/2*(A*b-2*a*B)*x^2/b^3+1/4*B*x^4/b^2-1/2*a^2*(A*b-a*B)/_
+ (b^4*(a+b*x^2))-1/2*a*(2*A*b-3*a*B)*log(a+b*x^2)/b^4
+--R
+--R
+--R (2)
+--R 2 2 2 2 3 2 3 6
+--R ((- 4A a b + 6B a b)x - 4A a b + 6B a )log(b x + a) + B b x
+--R +
+--R 3 2 4 2 2 2 2 3
+--R (2A b - 3B a b )x + (2A a b - 4B a b)x - 2A a b + 2B a
+--R /
+--R 5 2 4
+--R 4b x + 4a b
+--R Type: Expression(Integer)
+--E 414
+
+--S 415 of 1406
+a0:=integrate(t0,x)
+--R
+--R
+--R (3)
+--R 2 2 2 2 3 2 3 6
+--R ((- 4A a b + 6B a b)x - 4A a b + 6B a )log(b x + a) + B b x
+--R +
+--R 3 2 4 2 2 2 2 3
+--R (2A b - 3B a b )x + (2A a b